Morgan has three times as many pennies as quarters. If Morgan had three more quarters and seventeen fewer pennies, she would have the same number of each coin. How much money does she have?

Question

Genesis Allen · Accepted Answer

$2.80

Let's have #p="number of pennies"# and #q="number of quarters"#. Morgan is said to have three times as many pennies as quarters, therefore #p=3q# We are also informed that the quantity of coins would remain the same if she had three extra quarters and seventeen fewer pennies, so I can write: #p-17=q+3# Let's get started on the solution by changing the first equation into the second: #p-17=q+3# #(3q)-17=q+3# and now solve for #q#: #2q=20# #q=10# and now let's find #p# - we can substitute back into either of the original equations (I'll do both to show the answer is the same): #p=3q# #p=3(10)=30# additionally #p-17=q+3# #p-17=10+3# #p=30# The last question is: How much money does Morgan have? Using 30 pennies at a cost of one cent each and 10 quarters at a cost of 25 cents each, we get: #30($0.01)+10($0.25)=$0.30+$2.50=$2.80#

Savannah Anderson · Answer

undefined Let x = the number of quarters.  
Pennies: 3x  
Total value: $0.01(3x + 3) + $0.25(x - 17)