SOLUTION: I have this word problem and I am struggling with how to set it up. The problem is Mary took her children and some of their friends to Sneaky Pete's indoor amusement park. She boug

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Question 721662: I have this word problem and I am struggling with how to set it up. The problem is Mary took her children and some of their friends to Sneaky Pete's indoor amusement park. She bought 3 tickets to ride the go-carts and 4 tickets to play a game of bumper bowling. The total for all of those tickets was $39.75. If a ticket to play a game of bumper bowling was $1.75 less than twice the price of ticket to ride the go-carts, figure out the cost of a ticket to ride the go-carts and the cost of a ticket to play a game of bumper bowling. my first equation is 3g + 4b= 39.75, but I am struggling with the second one.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +g+ = the cost of a go-cart ticket
Let +b+ = the cost of a bumper-car ticket
(1) +3g+%2B+4b+=+39.75+
(2) +b+=+2g+-+1.75+
-------------------
(1) +300g+%2B+400b+=+3975+
Divide both sides by +25+
(1) +12g+%2B+16b+=+159+
and
(2) +2g+-+b+=+1.75+
(2) +200g+-+100b+=+175+
(2) +8g+-+4b+=+7+
------------------
Muyltiply both sides of (2) by +4+
and add (2) and (1)
(1) +12g+%2B+16b+=+159+
(2) +32g+-+16b+=+28+
+44g+=+187+
+g+=+4.25+
and, since
(2) +b+=+2g+-+1.75+
(2) +b+=+2%2A4.25+-+1.75+
(2) +b+=+8.5+-+1.75+
(2) +b+=+6.75+
The cost of a go-cart ticket is $4.25
The cost of a bumper-car ticket is $6.75
check:
(1) +3g+%2B+4b+=+39.75+
(1) +3%2A4.25+%2B+4%2A6.75+=+39.75+
(1) +12.75+%2B+27+=+39.75+
(1) +39.75+%2B+39.75+
OK