Question

without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions. two computer disks and three notebooks cost $25. however, five computer disks and four notebooks cost $52. find the price of each. which choice satisfies the given conditions? a. computer disk = $8; notebook = $3 b. computer disk = $3; notebook = $8 c. computer disk = $2; notebook = $9

Explanation:

To determine the correct choice, we check each option against the given conditions. Let \( d \) be the price of a computer disk and \( n \) be the price of a notebook. The conditions are:

1. \( 2d + 3n = 25 \)
2. \( 5d + 4n = 52 \)

• Option A: \( d = 8 \), \( n = 3 \)
• Check first condition: \( 2(8) + 3(3) = 16 + 9 = 25 \) (satisfies)
• Check second condition: \( 5(8) + 4(3) = 40 + 12 = 52 \) (satisfies)

• Option B: \( d = 3 \), \( n = 8 \)
• Check first condition: \( 2(3) + 3(8) = 6 + 24 = 30

eq 25 \) (does not satisfy)

• Option C: \( d = 2 \), \( n = 9 \)
• Check first condition: \( 2(2) + 3(9) = 4 + 27 = 31

eq 25 \) (does not satisfy)

Only Option A satisfies both conditions.

Answer:

A. computer disk = $8; notebook = $3