total of 43 coins in her purse. These coins are all quarters and nickels. If her change totals $7.75. How many nickels and quarters does she have?

Question

total of 43 coins in her purse. These coins are all quarters and nickels. If her change totals $7.75. How many nickels and quarters does she have?

Answer 1

Jenny this problem can be solve by setting up a system of 2 equations with two unknowns in which are the number of quarters and nickels.

 

Let q= the number of quarters

Let n=the number of nickels

 

q+n=43 This equations represents the total number of coins.

0.25q+0.05n=7.75 This equations represents her change totaling to $7.75.

 

Multiply the second equation by 100 to simplify the arithmetic.

 

q+n=43

25q+5n=775 Multiply the first equation by -5.

 

-5q-5n=-215

25q+5n=775 Add the two equation in which the n variable gets eliminated.

       20q=560 Divide both sides by 20.

 

           q=28 Substitute q=28 into the first equation and solve for n.

 28+n=43

-28     -28

       n=15 Therefore, she has 28 quarters and 15 nickels in her purse.

 

Hope this helps.