Answer: Choice B
44 practice, 113 machine, and 93 game balls
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Step-by-step explanation:
- x = number of practice baseballs
- y = number of pitching machine baseballs
- z = number of game balls
He bought 20 fewer game balls than pitching machine baseballs, which means,
z = y-20
Since the coach bought 250 baseballs total we can also write
x+y+z = 250
Let's replace z with y-20 and simplify
x+y+z = 250
x+y+y-20 = 250
x+2y = 250+20
x+2y = 270
Now let's calculate the subtotal costs for each type of baseball
- 1.75x = cost of just the practice baseballs
- 2.80y = cost of just the pitching machine baseballs
- 6.25z = cost of just the leather game balls.
Those subtotals add to this
1.75x+2.80y+6.25z = total cost = $974.65
1.75x+2.80y+6.25z = 974.65
Like before, I'll replace z with y-20
1.75x+2.80y+6.25(y-20) = 974.65
1.75x+2.80y+6.25y-125 = 974.65
1.75x+9.05y = 974.65+125
1.75x+9.05y = 1099.65
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So far we have this system of equations
I'll use substitution to solve the system.
Isolate x in equation (1)
x+2y = 270
x = 270-2y
Then plug this into equation (2) and solve for y.
1.75x+9.05y = 1099.65
1.75(270-2y)+9.05y = 1099.65
472.5-3.5y+9.05y = 1099.65
472.5+5.55y = 1099.65
5.55y = 1099.65-472.5
5.55y = 627.15
y = 627.15/5.55
y = 113
There are 113 pitching machine baseballs.
Use this y value to find x
x = 270-2y
x = 270-2(113)
x = 270-226
x = 44
There are 44 practice baseballs.
Also, we can say,
z = y-20
z = 113-20
z = 93
There are 93 game balls.
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Check:
x+y+z = 44+113+93 = 250 baseballs total
- A = 1.75*x = 1.75*44 = 77 = cost of just the practice baseballs
- B = 2.80*y = 2.80*113 = 316.40 = cost of just the pitching machine baseballs
- C = 6.25*z = 6.25*93 = 581.25 = cost of just the game balls
A+B+C = 77+316.40+581.25 = 974.65 = total cost
Everything checks out. Also note that value of z is 20 fewer than the value of y.