Question

Andrea has six times as many dimes as quarters. if her dimes and quarters total $12.75, how many of each coin does she have?

Answer 1

Since the question is asking for the no. of coins each, we can represent the numbers with variables.

number of quarters = x
number of dimes = 6x (because there as 6 times as many dimes as quarters)

Next we can multiply the variables by the value of each coin.

25x + 6(10)x = 1275
25x + 60x = 1275
(make sure the expressione quals 1275, not 12.75. A dime is not 10 dollars, nor is a quarter 25 dollars).
85x = 1275
x = 15

Now that we have the value for x, plug it back in.
Andrea has 15 quarters and 90 dimes.

Answer 2

x= number of quarters (worth $0.25)
6x= number of dimes (worth $0.10)

Multiply value per quarter by number of quarters. Multiply value per dime by number of dimes multiplied by 6 (because there are 6 times as many). Add those two sets together to equal $12.75.


0.25x + 6(0.10x)= $12.75
multiply 6 by parentheses

0.25x + 0.60x= 12.75
combine like terms

0.85x= 12.75
divide both sides by 0.85

x= 15 quarters


DIMES
= 6x
= 6(15)
= 90 dimes


CHECK
0.25x + 6(0.10x)= $12.75
0.25(15) + (6)(0.10)(15)= 12.75
3.75 + 9.00= 12.75
12.75= 12.75


ANSWER: There are 15 quarters and 90 dimes.

Hope this helps! :)