Question

Solve the problem by multiplying first. A clothing store is having a sale on shirts and jeans. Four shirts and two pairs of jeans cost $64. Five shirts and three pairs of jeans cost $87. The system of equations models this situation, where s is the cost of a shirt and j is the cost of a pair of jeans. How much does one shirt and one pair of jeans cost? 4s + 2j = 64 5s + 3j = 87

Answer 1

We will solve this by suing simultaneous equations,

⇒ 5s + 3j = 87

    4s + 2j = 64

Multiply the first equation with 4 and the second one with 5, this is to get one of the values equal so that we can cancel them out,

⇒ (5s + 3j = 87) × 4

    (4s + 2j = 64) × 5

∴ ⇒ 20s + 12j = 348

       20s + 10j = 320

Subtract both the equations. This is how your result (after subtraction) should look like,

  ⇒ 2j = 28

∴ ⇒ j = $14

Now replace the value of 'j' in one of the original equations,

⇒ 4s + 2(14) = 64

⇒ 4s + 28 = 64

⇒ 4s = 64 - 28

⇒ 4s = 36

∴ ⇒ s = $9

Therefore, one pair of jeans cost $14 and a shirt costs $9

Hope you understood! Feel free to ask me if you didn't understand a step.