Question

If one sweater and four shirts cost $43, while four sweaters and three shirts cost $81, find the price

Answer 1

To solve the problem, set up a system of equations. Multiply, subtract, and divide to find the prices of the sweater and shirt.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's assume the price of a sweater is 's' and the price of a shirt is 't'.

From the given information, we can write two equations:

1. Equation 1: s + 4t = 43
2. Equation 2: 4s + 3t = 81

We can solve this system of equations using substitution or elimination. Let's use elimination:

1. Multiply Equation 1 by 3 and Equation 2 by 4 to make the coefficients of 's' equal:

• 3s + 12t = 129
• 16s + 12t = 324

Subtract Equation 1 from Equation 2 to eliminate 't':

• (16s + 12t) - (3s + 12t) = 324 - 129
• 13s = 195

Divide both sides of the equation by 13:

• s = 15

Substitute the value of 's' back into Equation 1 or Equation 2 to find 't':

• 15 + 4t = 43
• 4t = 43 - 15
• 4t = 28
• t = 7

Therefore, the price of a sweater is $15 and the price of a shirt is $7.