SOLUTION: 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 ma

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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