Question

While shopping after her birthday, Annie bought 2 pairs of jeans and 3 shirts and spent $127. Her twin sister Hallie bought the same items consisting of 1 pair of jeans and 4 shirts and spent $116 how much does one pair of jeans cost and how much does a shirt cost

Answer 1

The shirt costs $21

Explanation:

2x + 3y = 127 ....eq 1

Her twin sister Hallie bought 1 pair of jeans and 4 shirts for $116.

So, x + 4y = 116 ....eq 2

Multiplying eq 2 by 2, we get :

2x + 8y = 232 ....eq 3

Subtracting eq 1 by eq 3, we get :

(2x + 8y) - (2x + 3y) = 232 - 127

5y = 105

Thus, y = 21

Putting this value of y in eq 2, we get :

x + 4(21) = 116

x = 116 - 84 = 32

Therefore, the cost of a pair of jeans = x = $32

And the cost of a shirt = $21

Answer 2

Let's use variables to represent the cost of one pair of jeans and the cost of one shirt.

Let's use j for the cost of one pair of jeans and s for the cost of one shirt.

From the problem, we know that:

2j + 3s = 127 (Annie's purchase)
1j + 4s = 116 (Hallie's purchase)

We can use these two equations to solve for j and s. One way to do this is to use substitution. Solving one of the equations for one of the variables and then substituting that expression into the other equation, we get:

j = 116 - 4s (from the second equation)
2(116 - 4s) + 3s = 127 (substituting into the first equation)

Simplifying and solving for s, we get:

232 - 8s + 3s = 127

-5s = -105

s = 21

Now that we know the cost of one shirt is $21, we can substitute that value back into one of the equations to solve for j:

1j + 4(21) = 116

1j + 84 = 116

1j = 32

Therefore, one pair of jeans costs $32.

So, the cost of one pair of jeans is $32 and the cost of one shirt is $21.