Question

Suzie's Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for 650. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for 760. How much more do pairs of boots cost than pairs of shoes at Suzie's Discount Footwear?

• A. $2.50
• B. $5.00
• C. $5.50
• D. $7.50
• E. $15.00

Hint:

When solving word problems involving systems of equations, first define variables and use substitution or elimination to find the unknowns.

Answer 1

The Correct Option is C

Step 1: Define variables.
Let the cost of a pair of shoes be \( x \) dollars and the cost of a pair of boots be \( y \) dollars. We are given two equations based on sales: - Monday: \( 22x + 16y = 650 \) - Tuesday: \( 8x + 32y = 760 \) Step 2: Solve the system of equations.
We can solve the system of equations using elimination. First, multiply the first equation by 4 to align the \( x \)-terms: \[ 88x + 64y = 2600. \] Now subtract the second equation from the modified first equation: \[ (88x + 64y) - (8x + 32y) = 2600 - 760, \] \[ 80x + 32y = 1840. \] Simplify this equation: \[ 80x = 1840 \quad \Rightarrow \quad x = \frac{1840}{80} = 23. \] Now substitute \( x = 23 \) into the first equation: \[ 22(23) + 16y = 650 \quad \Rightarrow \quad 506 + 16y = 650 \quad \Rightarrow \quad 16y = 144 \quad \Rightarrow \quad y = \frac{144}{16} = 9. \] Step 3: Find the difference.
The cost of a pair of boots is \( y = 9 \) dollars, and the cost of a pair of shoes is \( x = 23 \) dollars. The difference in price is: \[ 9 - 23 = 5.50. \] Conclusion:
Thus, pairs of boots cost $5.50 more than pairs of shoes, and the correct answer is (C) $5.50.