i need help in doing this problem

Question

joey had some 20 cent and 50 cent coins. 3/4 of the number of 20 cent coins is equal to 2/5 of the number of 50 cent coins. he had 42 more 50 cent coins than 20 cent coins. how many 20 cent coins did he have?

Answer 1

Hi Rick, let x represent the 20-cent coins and y represent the 50-cent coins. Then:

 

3 / 4 * x = 2 / 5 * y  : Equation 1

 

And:

 

y - 42 = x                : Equation 2

 

Substitute for x in equation 1:

 

3 / 4 * (y - 42) = 2 / 5 * y

 

Multiply the entire equation by 20 to clear the fractions:

 

15 * (y - 42) = 8y

 

15y - 630 = 8y

 

Rearrange the equation placing the y terms on one side and the constant on the other side:

 

15y - 8y = 630

 

7y = 630

 

Divide both sides by 7:

 

y = 90

 

Substitute for y in equation 2:

 

90 - 42 = x

 

x = 48

 

Solution:

 

Joey has 48 20-cent coins and 90 50-cent coins.

 

Check:

 

3 / 4 * 48 = 2 / 5 * 90

 

36 = 36, numbers check.

 

Questions?