To solve problems like this, you have to remember that there are two different kinds of data:
1) The NUMBER of each kind of coin
2) The monetary VALUE of each kind of coin.
#color(white)(....................)# . . . . . . . . . .
1) First find a way to express the NUMBER of each coin
Let #x# equal the number of quarters
Therefore, the number of dimes must be #32-x#
#x# #larr# number of quarters
#(32 - x)# #larr# number of dimes
#color(white)(....................)# . . . . . . . . . .
2) Next find a way to express the VALUE of each kind of coin
#x# quarters @ #25ȼ# ea . . . . . . #25x# #larr# value of the quarters
#(32 - x)# dimes @ #10ȼ# ea . . . #10(32 - x)# #larr# value of the dimes
#color(white)(....................)# . . . . . . . . . .
3) The sum of these values is #$5.60#
[value of quarters] + [value of dimes] = #$5.60#
[ . . . . . .#25x# . . . . . .] + [ . #10(32 - x)# .] = #560ȼ#
#25x + 10(32 - x) = 560#
Solve for #x#, already defined as "the number of quarters"
1) Clear the parentheses by distributing the #10#
#25x + 320 - 10x = 560#
2) Combine like terms
#15x + 320 = 560#
3) Subtract #320# from both sides to isolate the #15x# term
#15x = 240#
4) Divide both sides by #15# to isolate #x#, already defined as "the number of quarters"
#x = 16# #larr# answer for "the number of quarters"
If there are #16# quarters, there must be #16# dimes #larr# answer for "the number of dimes"
#color(white)(....................)# . . . . . . . . . .
Answer:
Jimmy has #16# dimes in his pocket
#color(white)(....................)# . . . . . . . . . .
Check
#16# quarters @ #25ȼ# ea . . . #$4.00#
#16# dimes #color(white)(..)#@ #10ȼ# ea . . . #$1.60#
——————————————
#32# coins . . . . . . . . . . . . . . . #$5.60#
#Check!#
