SOLUTION: An athletic director buys footballs, soccer balls, and softballs for their team. - Each football is 4 times as much as each softball - Each soccer ball is 10 dollars more than

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Question 1178653: An athletic director buys footballs, soccer balls, and softballs for their team.
- Each football is 4 times as much as each softball
- Each soccer ball is 10 dollars more than each football
- 10 footballs, 10 soccer balls, and 20 softballs total to a cost of 700 dollars.
**How much does each soccer ball cost?**
I came up with the equation 10x+10y+20z=700
x > football
y > soccer ball
z > softball
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

An athletic director buys footballs, soccer balls, and softballs for their team.
x > football
y > soccer ball
z+> softball
- Each football is 4 times as much as each softball
=> x=4z......eq.1
- Each soccer ball is 10 dollars more than each football
y=x%2B10 ....substitute x
y=4z%2B10 .........eq.2
if 10 footballs, 10 soccer balls, and 20 softballs total to a cost of 700 dollars, we have
10x%2B10y%2B20z=700......substitute x and y from eq.1 and eq.2
10%2A4z%2B10%284z%2B10%29%2B20z=700..........solve for z
40z%2B40z%2B100%2B20z=700
100z=700-100
100z=600
z=6
go to
x=4z......eq.1, substitute z
x=4%2A6
x=24
go to
y=4z%2B10 .........eq.2,substitute z
y=4%2A6%2B10
y=34
each soccer ball cost 34 dollars

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

An athletic director buys footballs, soccer balls, and softballs for their team.
- Each football is 4 times as much as each softball
- Each soccer ball is 10 dollars more than each football
- 10 footballs, 10 soccer balls, and 20 softballs total to a cost of 700 dollars.
**How much does each soccer ball cost?**
I came up with the equation 10x+10y+20z=700
x > football
y > soccer ball
z > softball
All you did was come up with an equation for the total cost of 10 footballs, 10 soccer balls, and 20 softballs,
after naming the number of footballs, soccer balls, and softballs, x, y, and z, respectively. 
It can't get any easier than the following:

Let cost of each softball, be S
Then cost of each football = 4S, and cost of each soccer ball = 4S + 10
We then get: 10(4S) + 10(4S + 10) + 20S = 700
40S + 40S + 100 + 20S = 700
100S = 600
Cost of 1 softball, or matrix%281%2C5%2C+S%2C+%22=%22%2C+600%2F100%2C+%22=%22%2C+%22%246%22%29%29
Cost of 1 soccer ball: highlight_green%28matrix%281%2C3%2C+4%286%29+%2B+10%2C+%22=%22%2C+%22%2434%22%29%29

OR

This METHOD will get you STRAIGHT to the cost of  a soccer ball.

Let cost of each soccer ball, be S
Then cost of each football = S - 10, and cost of a softball = matrix%281%2C3%2C+%281%2F4%29+%2A+%28S+-+10%29%2C+or%2C+%28S+-+10%29%2F4%29
We then get: 
Cost of 1 soccer ball, or