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.

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

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