Question

1. The ratio of the number of dimes to the number of pennies in a purse is 3 to 4. If 3 pennies are taken out of the purse, the number of dimes and the number of pennies in the purse will be equal. How many dimes are in the purse? (Answer key says 9- and if I multiply the ratio by three it makes sense. But how do I do this without guess and test method?)

Answer 1

d/p = 3/4
p-3 = d

p = 4d/3, so

4d/3 - 3 = d
d/3 = 3
d = 9