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Monty buys 8 pairs of jeans and 15 t-shirts for $193. steven buys 3 pairs of jeans and 12 t-shirts for $117. How much does each item cost?

a) Jeans: $18, T-shirt: $9
b) Jeans: $15, T-shirt: $8
c) Jeans: $14, T-shirt: $7
d) Jeans: $20, T-shirt: $6

1 Answer

5 votes

Final answer:

By setting up a system of equations and solving for the variables, the cost of each pair of jeans is found to be $25 and each t-shirt is $3.50, which is not reflected in the given multiple-choice options.

Step-by-step explanation:

Setting up a system of equations can solve this problem. Let J represent the cost of jeans and T represent the cost of t-shirts. We have two equations from the problem: 8J + 15T = $193 and 3J + 12T = $117. Solving the system of equations will give us the cost of each item.

To solve, multiply the second equation by -4 and add to the first equation to eliminate T: -12J - 48T = -468. Adding this to 8J + 15T = $193 gives us -4J - 33T = -275. Dividing by -1, we get 4J + 33T = $275. Since we want to solve for one variable at a time, multiply the adjusted second equation by 2 and add to the original first equation to get 11J = $275. Dividing by 11 we find J = $25. To find T, substitute J = $25 into the original second equation: 3($25) + 12T = $117, which simplifies to 75 + 12T = $117. Subtracting 75 from both sides, we get 12T = $42 and dividing by 12 we get T = $3.50.

Therefore, the cost of each jeans is $25 and each t-shirt costs $3.50, which is not one of the provided options, suggesting there might be an error in the question or the options.

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