SOLUTION: three footballs and one soccer ball cost $155. Two footballs and three soccer balls cost $220. Determine the cost of one football and the cost of one soccer ball.

Question 101847: three footballs and one soccer ball cost $155. Two footballs and three soccer balls cost $220. Determine the cost of one football and the cost of one soccer ball.
Answer by doukungfoo(195) (Show Source): You can put this solution on YOUR website!
first set some variables
Let f = football cost
and
Let s = soccer ball cost
Now write equations from the given information
Given: three footballs and one soccer ball cost $155
ok so using the variables f and s lets write and equation
3f + s = 155
Now what else are we given?
Given: two footballs and three soccer balls cost $220
write an equation
2f + 3s = 220
Ok now we have a system of equations that we can use to solve for f and s
Take the first equation and set it equal to s
3f + s = 155
s = 155 - 3f
Now that we have s equal to 155-3f we can substitiute that into the second equation. Here goes...
2f + 3s = 220
2f + 3(155-3f) = 220
now we have an equation with one variable that we can solve for.
2f + 3(155-3f) = 220
distribute 3 across (155-3f)
or in other words multiply 3 times 155 and 3 times -3f
2f + 465 - 9f = 220
combine like terms
465 - 7f = 220
subtract 465 form both sides of the equation
465 - 465 - 7f = 220 - 465
-7f = -245
divide both sidse of the equation by -7
-7f/-7 = -245/-7
f = 35
Answer: One football costs $35.00
Now we can use this value for f to solve for s
Take the first equation and substitute f with 35
3f + s = 155
3(35) + s = 155
multiply 3 times 35
105 + s = 155
subtract 105 from both sides of the equation
105 - 105 + s = 155 -105
s = 50
Answer: One soccer ball costs $50.00
Check the answers by trying them in both of our orignal equations
3f + s = 155
3(35) + 50 = 155
105 + 50 = 155
155 = 155
That works lets try the second equation
2f + 3s = 220
2(35) + 3(50) = 220
70 + 150 = 220
220 = 220
That works too.
Conclusion:
We solved the system of equations by using the substitution method and checked our answers to prove them correct.

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