Clara has 8 coins worth 17¢. if the coins are all dimes and pennies, how many dimes and pennies does she have?

One dime, seven pennies

Let x = the number of dimes

Let y = the number of pennies.

There are 8 coins, therefore

x + y = 8 (1)

The coins are worth 17 cents, therefore

10x + y = 17 (2)

Subtract equation (1) from equation (2).

10x + y - (x + y) = 17 - 8

9x = 9

x = 1

From (1), obtain

y = 8 - x = 8 - 1 = 7

Answer: 1 dime, 7 pennies.