A coin purse contains dimes and quarters The number of dimes

A coin purse contains dimes and quarters. The number of dimes is 5 less than twice the number of quarters. The total value is $4.00. Find the number od dimes and quarters.

Part A. Interpret the question and express the problem in Mathematical language.

Part B. Procedural Math.

Solution

Total value = 4.00, let d = number of dimes, let q= number of quarters

We have also been given that d = 2q - 5

Total value = (0.10)(d) + (0.25)(q) = 4.00

Since d = 2q - 5, substitute for d
(0.10)(2q - 5) + 0.25q = 4.00

Distribute the 0.10 to get 0.20q -0.50 + 0.25q = 4.00

Combine like terms to get 0.45q - 0.50 = 4.00

0.45q = 4.50

q = 10 d = 2q - 5
d = 15

There are 15 dimes and 10 quarters.