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!#