Question

Bea has dimes and quarters in the ratio of 1:4. If 22 of her coins are dimes, how many quarters does she have?​

Answer 1

Let the number of dimes that Bea has be represented by x, and the number of quarters be represented by y. Since the ratio of dimes to quarters is 1:4, we can write:

x:y = 1:4

This can also be written as:

x = (1/5)y

We know that Bea has a total of 22 coins, so we can write:

x + y = 22

Substituting the first equation into the second equation, we get:

(1/5)y + y = 22

Multiplying both sides by 5 to eliminate the fraction, we get:

y + 5y = 110

Simplifying the equation, we get:

6y = 110

Dividing both sides by 6, we get:

y = 18.33

Since the number of quarters must be a whole number, we round up to the nearest integer:

y = 19

Substituting this value back into the first equation, we get:

x = (1/5)(19) = 3.8

Again, since the number of dimes must be a whole number, we round up to the nearest integer:

x = 4

Therefore, Bea has 4 dimes and 19 quarters.

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