Hank saves $5.50 in dimes and quarters over a week. he has 20 more dimes than quarters. find the number of dimes and quarters he saves.

Question

i was doing this problem in algabra class and i got stuck on it

 

Answer 1

Hi Keith, let x represent the quarters. Then x + 20 equals the number of dimes. We can set up an equation with this information and the fact he saves $5.50 each week.

 

The equation:

 

Each quarter is equal to .25 and each dime is equal to .10. We use these values in the equation.

 

x * .25 + (x + 20) * .10 = 5.50

 

.25x + .10x + 2 = 5.50

 

I do not like to work with fractions or decimals. To clear the decimals in the equation, multiply each term by 100:

 

25 + 10x + 200 = 550

 

35x + 200 = 550

 

Subtract 200 from both sides giving:

 

35x = 350

 

Divide both sides by 35 gives:

 

x = 10, or Hank saves 10 quarters each week.

 

The number of dimes Hank saves is x + 20, or 10 + 20 = 30.

 

Solution:

 

Hank saves 10 quarters and 30 dimes each week.

 

Check:

 

10 quarters equals $2.50, and 30 dimes equals $3.00. 

 

Total saved: $2.50 + $3.00 = $5.50, the numbers check.

 

Questions?