Question

without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions. kesha has a total of 90 coins, all of which are either dimes or quarters. the total value of the coins is $12.00. find the number of each type of coin. which choice satisfies the given conditions? a. 70 dimes; 20 quarters b. 60 dimes; 30 quarters c. 30 dimes; 36 quarters

Explanation:

Step1: Check total number of coins

For each option, sum the number of dimes and quarters to see if it equals 90.

• Option A: \(70 + 20 = 90\) (satisfies total coins)
• Option B: \(60 + 30 = 90\) (satisfies total coins)
• Option C: \(30 + 36 = 66

eq90\) (does not satisfy, eliminate)

Step2: Check total value of coins

Calculate total value (in dollars) for remaining options. Dime = $0.10, Quarter = $0.25.

• Option A: \(70\times0.10 + 20\times0.25 = 7 + 5 = 12\) (satisfies total value)
• Option B: \(60\times0.10 + 30\times0.25 = 6 + 7.5 = 13.5

eq12\) (does not satisfy)

Answer:

A. 70 dimes; 20 quarters