Question 1169119: On Monday morning, Mr. Descartes asked his Algebra students whether they had gone to the carnival in town over the weekend."did," said Kristen. "I went on the Teacups ride twice, the rollercoaster twice, and the Spinning Vortex once. I had a lot of fun for only $20. went on those rides, too!exclaimed Jorge. "Just once each on the Teacups and rollercoaster, but three times on the Spinning Vortex, all for $25.did five Teacup rides," said Lakesha. "And two rollercoaster rides, and one Spinning Vortex. I spent $29."Marc listed off the same rides. "Three Teacups for me, plus two rollercoasters , plus two rides on the Spinning Vortex, all for You don't need to say " interrupted Mr. Descartes , "I know how much you spent ." How much are the rides? How much did Marc spend? And how much is each ride?
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi here,
Make Tea cups = x
Roller coaster = y
and Spinning Vortex = z
Kristen => 2x + 2y + z = 20
Jorge => x + y + 3z = 25
Lakesha => 5x + 2y + z = 29
2x + 2y + z = 20.....(1)
x + y + 3z = 25......(2)
5x + 2y + z = 29......(3)
Subtract Eq(1) from Eq(3)
2x + 2y +z = 20
5x + 2y + z = 29
3x = 9
x = 3
Substitute x = 3 in Eq(2)
x + y + 3z = 25
3 + y + 3z = 25
y + 3z = 22 .......(4)
Substitute x = 3 in Eq(3)
5x + 2y + z = 29
5(3) + 2y + z = 29
15 + 2y + z = 29
2y + z = 14........(5)
Using Eq(4) and (5)
y + 3z = 22.......(4)
2y + z = 14.......(5)
Multiply Eq(4) by 2
2y + 6z = 44......(4)
2y + z = 14.......(5)
Subtract Eq(5) from (4)
5z = 30
z = 6
Substitute z = 6 into y + 3z = 22
y + 3(6) = 22
y + 18 = 22
y = 4
Teacups cost $3 Roller coaster cost $4 Spinning Vortex cost $6
Marc spent 3 Tea cups 3(3) = $9 + 2 Roller coaster 2(4) = $8
and 2 Spinning Vortex = 2(6) = $12
Total = $29
Hope this helps :-)
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