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At a basketball game, A team made 56 successful shots. They were a combination of 1-point and 2-point shots. The team scored 95 points in all. Right and solve a system of equations to find the number of each type of shot.

QUESTION:

There were____ 2-point shorts and____ 1-point shots.

1 Answer

2 votes

Answer:

95/3 = 31

31 ratio for 2 and 1 then make up the difference

there were 25 point and 45 ...1 point shots

but 32 x 3 makes 96 you will see the top answer is correct 25 2 points and 45 one points as we can distribute 50 and 45 easily as a fair 6/10 and 4/10 balance of 95 just like we do to find 60% of 95 or 40% of 95.

Hi Samantha heres an example for both questions see if you can try add the items and find a multiple to 95 for this question then divide by 3 and distribute like this example below which answers your other question about popcorn.

Explanation:

462 = revenue

282 = amount sold

$1 = small

$3 = large

1. we add the amounts together = $4

2. We divide 462/4 = 460/4 = 115 so we are 2 out

3. In our workings we show 4 less +2 less = 4 x 115 = 460 +2 =462-6

456

111 = small $1

456-111 = 345 + 6 = 351 ( large $3 as we were 4+2 less we add 6 = 351

351/3 = 119 large. (we divide by price $3)

111 = small.(we keep)

To find equations

we know know on our workings we have 111 +351 we can call these s and l

s111 + l351 = s111 + l119

462 = 230

462/230 = 2sl mean price.

=====

We plug in again to find 1

462/230 + 1 = 2sl(+l)+x

1s x 1^2 x 1l^2 x x = 1 we rearrange the 1

1s x 1^2 x 3l we replace ^2 with 1

1s x 1 x 3l = 1

1 x 3l = 1/1s

3l = 1s

====

Now we can match s and l

3 / 1 + 4 = 460l

3 / 1 = 460/4l

3 / 1 = 120l

1 x 120-3l

1 x 117l

117 ( 351/3) = L you cna try rewriting this ( ) plug in in a new equation just added to show you how it works.

l = 357 = L I wrote capitals as the l looked like a number.

When we subtract total 462- 351 = s then s = 111

When you understand minus 6 may have made things more tricky try another number where the total 462 is rounded up by 3 to 465 or 470 an work in 30's and 10's then divide by 10 may be of some help/reflection to designing equations it helps you remember alternatives to find out distribution.

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