A man has 25 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 370 cents, how many dimes and how many quarters does he have?
x = number of quarters
25 - x = number of dimes {there are a total of 25 coins}
25x + 10(25 - x) = 370 {value of coin multiplied by number of coins equals total value}
25x + 250 - 10x = 370 {used distributive property}
15x + 250 = 370 {combined like terms}
15x = 120 {subtracted 250 from each side}
x = 8 {divided each side by 15}
25 - x = 17 {substituted 8, in for x, into 25 - x}
8 quarters
17 dimes
unless there is, at least, 1 hole in a pocket
- Algebra House
25 - x = number of dimes {there are a total of 25 coins}
25x + 10(25 - x) = 370 {value of coin multiplied by number of coins equals total value}
25x + 250 - 10x = 370 {used distributive property}
15x + 250 = 370 {combined like terms}
15x = 120 {subtracted 250 from each side}
x = 8 {divided each side by 15}
25 - x = 17 {substituted 8, in for x, into 25 - x}
8 quarters
17 dimes
unless there is, at least, 1 hole in a pocket
- Algebra House
