How many free throws had she attempted before the last game?

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11dogs

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Can someone please help me set up two equations to figure this problem out?
Celcilia made 75% of her free throws before the last basketball game of the season. In the last game she shot 4 free throws and made one of them, lowering her percentage to 65%. How many free throws had she attempted before the last game? I know the answer (she made 12 out of 16 free throws) by using guess and check but I need to equations for my homework assignment.
 
Re: Word problems

There are many different ways to set this up. I see it this way.
First, start by naming things completely.

Let A = number of free throws attempted prior to the last game.
Let n = number of free throws made prior to the last game.

Now use these two statements to build your equations.

Celcilia made 75% of her free throws before the last basketball game of the season >>> means 75% of the total number of free throws attempted prior to the last game is the number of free throws made prior to the last game.

In the last game she shot 4 free throws and made one of them, lowering her percentage to 65% >>> means 65% of the total attempts (prior to last game plus last game) equals number made prior to the last game plus number made in last game.

Give it a try and come back for more help if you need to. If you come back, please show us what you have done so far.
 
Re: Word problems

Well here's what I have so far:
M=the free throws that she made
T=the total free throws

M+1 divided by T+4=.65
M divided by T=.75

p.s. I'm not sure how to illustrate the equations here so I'm using words instead
 
Re: Word problems

11dogs said:
Can someone please help me set up two equations to figure this problem out?
Celcilia made 75% of her free throws before the last basketball game of the season. In the last game she shot 4 free throws and made one of them, lowering her percentage to 65%. How many free throws had she attempted before the last game? I know the answer (she made 12 out of 16 free throws) by using guess and check but I need to equations for my homework assignment.
Click to expand...

The first thing you need to do is NAME things (thanks, Tkhunny!)

What is it that you are trying to find? The question asks, "how many free throws had she attempted before the last game?" Since this is what you are looking for, it makes sense (to me, at least) to choose a variable to represent this number:

Let f = number of free throws attempted before the last game

Before that last game, she had MADE 75% of the free throws she attempted. So,

free throws made before last game = 75% of f
free throws made before last game = 0.75f

She attempted 4 free throws in the last game. So, in the whole season, she attempted (f + 4) free throws. And at the end of the season, she had made 65% of of the attempted free throws, or 0.65(f + 4)

We know she MADE 1 free throw in that last game. She'd made 0.75f free throws in the season before the last game, and made 1 free throw in that game. So in the whole season, she made 0.75f + 1 free throws.

free throws made before last game + free throws made in last game = 65% of free throw attempts for whole season

0.75f + 1 = 0.65(f + 4)

Now, solve that for f...which we have defined to be the number of free throws she had attempted before the last game of the season.
 
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