You go shopping at a local department store with your friend and cousin. You buy one pair of jeans, four pairs of shorts, and two shirts for $84. Your friend buys two pairs of jeans, one pair of shorts, and three shirts for $76. Your cousin buys one pair of jeans, two pairs of shorts, and one shirt for $52. How much does each item cost?

Answers

Answer 1

Answer: Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8

Step-by-step explanation:

Let x= cost per pair of jeans

y = Cost per pair of shorts

z= cost per shirt.

For you, total cost = x+4y+2z= 84

For your friend,  total cost = 2x+y+3z=76

For cousin, total cost = x+2y+z= 52

Required system:

[tex]x+4y+2z=84\ (i)\\ 2x+y+3z=76\ (ii)\\ x+2y+z=52\ (iii)[/tex]

from (i), [tex]x=84-4y-2z[/tex]    (*)

put this in (ii) and (iii) we get

[tex]2\left(84-4y-2z\right)+y+3z=76\\\Rightarrow\ -7y-z+168=76\ (iv)\\\\ 84-4y-2z+2y+z=52\\\Rightarrow\ -2y-z+84=52 \ (v)[/tex]

from (iv), [tex]y=-\frac{z-92}{7}\ (vi)[/tex]

[tex]\mathrm{Subsititute\:}y=-\frac{z-92}{7}\ \text{in}\ (v)[/tex]

[tex]-2\left(-\frac{z-92}{7}\right)-z+84=52\\\\\Rightarrow\ -2\left(-\frac{z-92}{7}\right)-z=-32\\\\\Rightarrow\ -\frac{5z}{7}-\frac{184}{7}=-32\\\\\Rightarrow\ -5z-184=-224\\\\\Rightarrow\ -5z=-40\\\\\Rightarrow\ z=8[/tex]

[tex]\mathrm{Subsititute\:}z=8\text{ in (vi)}[/tex]

[tex]y=-\frac{8-92}{7}\\\\\Rightarrow \ y=12[/tex]

[tex]\mathrm{Subsititute\:}z=8,\:y=12\text{ in (*)}[/tex]

[tex]x=84-4\cdot \:12-2\cdot \:8\\\\\Rightarrow\ x= 20[/tex]

Hence, x= 20, y= 12 , z=8

So, Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8


Related Questions

True or False: In a ratio table, the ratios are equivalent.

Answers

Answer: True

Step-by-step explanation:

Katie and Mina both commute to work. Katie's commute on the train takes 10 minutes more than one half as many minutes as Mina's commute by car. It takes Katie 30 minutes to get to work. Write an equation to determine how many minutes it takes Mina to get to work. NEED HELP PLZZ :)

A 30 = one halfx + 10
B 30 = one halfx − 10
C 30 = 2x − 10
D 30 = 2x + 10

Answers

The answer is A! Good luck!

Answer:

A) 30 = (1/2)x + 10

Step-by-step explanation:

PLEASE HELP NOW!!!!
WILL MARK BRAINLIEST AND ALL THAT JAZZ!!




The rule for significant digits in multiplication is, the answer should reflect the number in the problem with the
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b. fewest significant digits
a. Most significant digits

Answers

Answer:

b

Step-by-step explanation:

BCCCCCC

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If you have an even integer on a number line which we will call "x", what could you call the next consecutive number? What could you call the next consecutive even integer on the number line?

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Answer:I NEED THE ANSWER TO

Step-by-step explanation:

Answer:

x+2

Step-by-step explanation:

what is a minimum number of points required to mark all maximum, minimum and zeros in a period of a sinusoid?

Answers

Answer:5 points :)

Step-by-step explanation:= −1) and 3 zeros (sin(0) = 0,sin( ) = 0, sin(2 ) = 0). Answer: 5 points. Hope this helps!

e. How many feet are there in 14.0 yards? (3 ft = 1 yd)

Answers

Answer:

42

Step-by-step explanation:

i smart

Answer:

Step-by-step explanation:

1 yard = 3 ft

To find 14 yards, just multiply 14 by 3

14 yards = 14 x 3 = 42 ft

is {(9,- 15), (0, 0), (4,0), {9, 2)} a function​

Answers

Answer:

no im pretty sure they are not functions

Correct me if im wrong also learning

ASAP PLEASE What is the slope of the blue and green line ( both parallel)

Answers

Answer:

slope = - 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 8, 4) and (x₂, y₂ ) = (- 1, - 10) ← 2 points on the green line

m = [tex]\frac{-10-4}{-1+8}[/tex] = [tex]\frac{-14}{7}[/tex] = - 2

Repeat with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, - 6) ← 2 points on the blue line

m = [tex]\frac{-6-0}{0+3}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2

Since the slopes are equal then the lines are parallel

what’s 40/44 in lowest terms

Answers

Answer:10/11

Step-by-step explanation:i think you mean in simpilest terms so here is that! hope this helped:)

Jessica has 7/8 of a pound of candy.She are 1/4 of it at the movies. How much does she have left over
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B. 4/8
C. 3/4
D. 1/2​

Answers

Answer: A. 5/8

1/4 x 2 will equal 2/8. 7/8 - 2/8 = 5/8

Answer:

A. 5/8

Jessica has 5/8 pounds of candy left

✨Step-by-step explanation:✨

7/8 (how many pounds she used to have) - 1/4 (how much she ate at the movies) = ?

✨To make this easier let us turn 1/4 into 2/8 (both fractions are equivalent):✨

7/8 (How many pounds she used to have) - 2/8 ([Also 1/4] how much she ate at the movies) = 5/8 (how much she has left)

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The answer is bbbb......

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Answer:

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Answers

Answer: 5√10.

Step-by-step explanation:

250 is split into its prime factors as 2 * 5 * 5 * 5 which implies √250 = √(2 * 5 * 5 * 5). Now we can simplify this further by pulling out the number which is multiplied to itself. This gives √250 = 5 * √(2 * 5) = 5√10. Therefore the square root of 250 is √250 = 5√10.

what is the chang in temperture from -24 to 15?

Answers

Answer:

38 degree difference

Step-by-step explanation:

24 + 15 =39

But they share the 0 degree spot so minus one.

39-1=38

A small lizard 5/8 inch long.a larger lizard is 5 1/5 times as long.how long is the larger lizard??

Answers

Answer:

3.25 inches

Step-by-step explanation:

5/8 = .625

5 1/5 = 5.2

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are two parallelograms with the same side lengths
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Answers

Answer:

Step-by-step explanation:

most of the time yes

What’s is 93875748282858828819482 - 3826283 have fun

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Answer:

9.3875748e+22

Step-by-step explanation:

which line has a constant of proportionality between y and x of 5

Answers

Answer:

tp

Step-by-step explanation:

The constant of proportionality between y and x of 5 for line A.

What is the slope of straight line?

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.

The negative slope indicates the rate of decrease while the positive shows the rate of increase.

The lines in the graph are passing through origin.

It implies that the y-intercept for all the lines is zero.

The slope-intercept equation of the line can be written as,

y = mx + c

Here c is the y-intercept.

When c = 0, the equation becomes as y = mx.

It implies that the for lines passing through origin, the slope of the line becomes the proportionality constant.

Now, from the given graph the line A is shown to be passing through (5, 1).

Then, the slope is given as,

m = (5 - 0)/(1 - 0) = 5

Hence, the line A in the given graph has constant of proportionality as 5.

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ANSWER PLZZ!!
Your neighbor Sally wants to plant flowers around the edge of her circular above ground pool. If the diameter of Sally’s Pool is 18ft, how many flowers will sally need to plant to surround the pool? Round your answer to the nearest hundredth

Answers

Answer:

This answer involves finding the circumference of the circle which is basically the length of the entire perimeter of the garden

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Circumference = 2 * pi * radius

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Is 7/16 of a mile repeating or terminating

Answers

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Terminating.

Step-by-step explanation:

.4375 miles is terminating.

Answer:

terminating

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it's 0.3475

which statement about the following system of inequalities is true? y-2x<2.5

Answers

The first one ;)

Haha a good day

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Answers

Distributive property is an example like this

2(x+y)=2x+2y.

a(b+c)= ab+ac

Answer:

You dont have the equation

>:(

Step-by-step explanation:

YOOO HELP‼️

What is the slope of the line represented by the equation -52 + 2y = 10?

Answers

Answer:

5/2

Step-by-step explanation:

Use PEMDAS to solve the equation in y=mx+b form.

Add 5x on each side of the = sign  (which cancels on left side, and add on right)

Your equation should look like this: 2y=5x+10

Next, you're going to divide the whole equation by 2, to get y by itself

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B= y-intercept

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Answers

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Answers

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Step-by-step explanation:

i used a calculator

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Answers

Answer

x^(2)    x to the second power

Step-by-step explanation:

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Answers

Thing I no this one I just forgot

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Please help me!!!

Answers

Answer:

957

Step-by-step explanation:

The largest three-digit multiple of 33 * 30 is 990, which uses only two different digits. Now we work backwards: Subtracting 33 once gives 990-33=957, which has three different digits. Therefore, our answer is 957

957 is the greatest three-digit number which is multiplied by 33.

What are digits?

A numerical digit is a single sign that can be used alone or in combination to denote a number in a positional numeral system.

A digit is a component of a set that, when put together, forms a numerical system.

Examples of digits include 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

If we multiply 33 by 31

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Now trying to multiply less than 31

By 30

33 × 30 = 990 but here two digits are the same.

By 29

33 × 29 = 957 and all three are different.

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(MC 02.03)

What set of reflections and rotations would carry rectangle ABCD onto itself?

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Rotate 180°, reflect over the x-axis, reflect over the line y=x

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Answers

Answer:1st option

Step-by-step explanation:

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Answers

Answer:

4.27x10^2

Step-by-step explanation:

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