Question 1130121: I have been stuck trying to solve this for quite some time and is still having difficulty finding the correct solutions. Could someone please help. Thank you
Last year, at Haven's Pond Car Dealership, for a particular model of BMW, Jeep, and Toyota, one could purchase all three cars for a total of $140,000. This year, due to inflation, the same cars would cost $151,830. The cost of the BMW increased by 9%, the Jeep by 5%, and the Toyota by 11%. If the price of last year's Jeep was $7,000 less than the price of last year's BMW, what was the price of each of the three cars last year? (Round your answers to the nearest integer.)
This is my work and answers I've gotten which are incorrect.
1.09B +1.05J +1.11T= 151, 830
B+J+T=140, 000
J+7000= B
B+J+T= 140,000
(J+7000)+J+T=140,000
2J+T=130,000
1.09B+1.05J+1.11T=151, 830
1.09(J+7000)+1.05J+1.11T=151, 830
1.09J+7630+1.05J+1.11T=151, 830
2.14J+1.11T=144, 200
2J+T=130,000
2.14J+1.11T=144, 200
-1.11(2J+T=130, 000)
(-2.22J-1.11T=147, 630)
+(2.14J+1.11T= 144, 200)
J=4288
2J+T=130, 000
2(4288)+ T= 130, 000
8576+T=130,000
t=124,424
4, 288-124,424= 120,136
BMW= 120, 136. J=4288. Toyota: 4288.
Found 2 solutions by math_helper, stanbon:
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! This is my work and answers I've gotten which are incorrect.
1.09B +1.05J +1.11T= 151, 830
B+J+T=140, 000
J+7000= B
B+J+T= 140,000
(J+7000)+J+T=140,000
2J+T=130,000 <<<——<<<<< 2J + T = 133000
1.09B+1.05J+1.11T=151, 830
1.09(J+7000)+1.05J+1.11T=151, 830
1.09J+7630+1.05J+1.11T=151, 830
2.14J+1.11T=144, 200
2J+T=130,000
2.14J+1.11T=144, 200
-1.11(2J+T=130, 000)
(-2.22J-1.11T=147, 630)
+(2.14J+1.11T= 144, 200)
J=4288
2J+T=130, 000
2(4288)+ T= 130, 000
8576+T=130,000
t=124,424
4, 288-124,424= 120,136
BMW= 120, 136. J=4288. Toyota: 4288.
—————
. . .
2J+T=130,000 <<<——<<<<< 2J + T = 133000
1.09B+1.05J+1.11T=151, 830
1.09(J+7000)+1.05J+1.11T=151830
2.14J+1.11T=144200 (*)
Here, I would substitute "133000-2J" from the corrected line for "T" in the line (*):
2.14J + 1.11(133000-2J) = 144200
Solve for J, then the others follow easily enough.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Last year, at Haven's Pond Car Dealership, for a particular model of BMW, Jeep, and Toyota, one could purchase all three cars for a total of $140,000. This year, due to inflation, the same cars would cost $151,830. The cost of the BMW increased by 9%, the Jeep by 5%, and the Toyota by 11%. If the price of last year's Jeep was $7,000 less than the price of last year's BMW, what was the price of each of the three cars last year? (Round your answers to the nearest integer.)
This is my work and answers I've gotten which are incorrect.
1.09B +1.05J +1.11T= 151,830
B +J +T = 140,000
B -J +0T = 7000
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Using a TI-84 Matrix-solving function I get:
B = 49875
J = 42875
T = 47250
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Cheers,
Stan H.
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