1 answer

Jimmy has a pocket full of quarters and dimes. There are a total of 32 coins. When he added it

Question:

Jimmy has a pocket full of quarters and dimes. There are a total of 32 coins. When he added it up he counted $5.60 How many dimes does he have in his pocket?

Answers

Jimmy has #16# dimes in his pocket.

(And #16# quarters too)

Explanation:

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!#

.

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