Question 1108816: Mira is playing a game where she is trying to toss a ball into a large basket or a small basket. The large basket is worth 2 points, and the small basket is worth 3 points. Mira made 15 baskets for a total of 35 points. If x represents the number of large baskets made and y represents the number of small baskets made, how many large baskets did she make?
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
From the condition, you have this system of two equations in two unknowns
x + y = 15, (1)
2x + 3y = 35. (2)
From equation (1), express y = 15-x and substitute it into equation (2), replacing y.
In this way, you will get a single equation for only one unknown x, which is your main interest.
2x + 3*(15-x) = 35. (It is how the Substitution method works.)
Simplify and solve it for x:
2x + 45 - 3x = 35 ====> -x = 35 - 45 ====> -x = -10 ====> x = 10.
Answer. 10 large baskets.
Solved.
On the way, you learned on how the Substitution method works.
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