Algebra/Word Problems into equations
Im trying to help my mathematically challenged daughter with her homework and its been so long since I did it, Im having trouble too. I have helped her with 6 but we have 4 more we are stuck on. We can work them out (Substitution Method) but turning the word problems into two equations (or more) is what we are having trouble with. If you could help, that would be great! Here are the ones that we are stuck on:
#1: 195 Students went on a field trip. They took 7 vehicles, some cars and some buses. Each car holds 5 students and each bus holds 45 students. Find the number of cars and the number of buses they took.
#2: At the end of the 2000 WNBA regular season, The Houston Comets had 22 more victories than losses. The number of victories they had was three less than six times the number of losses. How many regular season games did the Houston Comets play during the season.
#3: All 231 students in the French class went on a field trip. Some students rode in vans which hold 7 studentseach and some rode in buses that hold 25 students each. How many of each type of vehicle did they use if there were 15 vehicles total?
#4: Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. Write a system of equations to represent this situation. How many adult tickets and student tickets were bought?
Thank you so much for taking your time to help :)
I will turn them into equations, and then you can solve them.
#1 Let x be the number of busses. The number of cars, then, is 7-x.
This gives 45x + 5(7-x) = 195.
Multiply out the 5(7-x) to get 35 - 5x.
Combine 45x - 5x into one term, and subtract 35 from both sides.
Divide this by 40, and that's the answer.
#2 Let x be the number of victories.
The makes the number of losses be x-22.
The other equation is is x = 6(x-22)-3.
Multiply by the 6 gettting 6x - 132, combine like terms, subtract 6x from both sides of the equation, divide by the coefficient in front of x, and that's the answer.
#3: Let x be the number of buses. This means that there are 15-x vans.
The equation is then 25x + 7(15-x) = 231.
Multiply 7(15-x) to get 105-7x, combine x's on left and subtract off the 105 from both sides.
Do some division, and you have x.
#4: Let x be the number of adults. Since the group of friends purchased 8 tickets,
and there were x adults, this means there were 8-x children. Take 7.25*x + 5.50(8-x) = 52.75.
Multiply, put the like terms together, and divide by the constant.