# Math Question: Luke bought a pair of socks, a pair of pants and a jacket. The jacket cost four times as much as the pants and the socks cost $7. Luke spent a total of $187. If P represents the cost of the pants, write an equation to match the story and find the cost of the jacket.

Asked By Eric On 05/21/2020 20:32

## Math Answers

Luke bought 3 things: 1 socks, 1 pants, 1 jacket.
Let s be the price of the socks in $, p and j the price of the pants and jacket in $.
s=$7 - this is given
s+p+j=$187 - this is given
since s=$7 we can substitute $7 for s:
s+p+j=$187
$7+p+j=$187
We can then subtract $7 from both sides:
$7-$7+p+j=$187-$7
0+p+j=$180
We can also subtract $7 FIRST:
s+p+j=$187
s-$7+p+j=$180-$7
(s-$7)+p+j=$180
($7-$7)+p+j=180, which is the same.
We now know that p+j=$180. We know that because we were told that the jacket costs four times as much as the pants, or:
j=4p
if p=1 then j=4, if p=20 then j=80, etc.
Using both these equations:
j=4p
p+j=$180
we can substitute:
j+p=$180
(j)+p=$180
(4p)+p=$180
4p+p=$180
5p=$180
then divide both sides by 5:
5p/5 = $180/5
p=$36
We know know:
s=$7
p=$36
j=4p
s+p+j=$180
taking the second two:
p=$36
j=4p
we substitute:
j=4p
j=4(p)
j=4($36)
j=4(3*$12)
j=12*$12
=$144
checking our work:
144/4=36
so j=4p
j+p+s=
$144+$36+$7=
$140+$4+$6+$30+$7=
$140+$10+$30+$7=
$140+$40+$7=
$180+$7=
$187
so
s=$7
p=$36
j=$144
or
The socks cost $7, the pants cost $36 and the jacket $144.

Answered On 05/27/2020 11:50

Answered On 05/27/2020 11:50

You set up P (pants) =1/4 J (jacket) as one equation. Then the second equation is P+J+7 =187. By substituting 1/4 J for P in the second equation, you get 1/4PJ+J + 7 =187. This equation simplifies to J= 720/5, and then J=$144. So the jacket cost $144. Always a good idea to check your answer, so the second equation becomes 36+144+7=187, and that is what Luke spent! Hope that helps.

Answered On 05/27/2020 15:21

Answered On 05/27/2020 15:21

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