Question

Allison's team scored 78 points in total. Nineteen of the baskets counted 1 point each. The remaining 27 baskets we're 2 point and 3 point shots. How many of each kind of shot did the team make?

Answer 1

Answer:

1 point baskets = 19

2 point baskets = 22

3 point baskets = 5

Step-by-step explanation:

Given:

Number of points scored (P) = 78

Number of 1 point baskets = 19

Number of 2 and 3 points basket = 27

Let the number of 2 point baskets be 'x' and 3 point basket be 'y'.

Therefore,

$x+ y=27\\\\y=27-x$

Now, points scored per 2 point basket = 2

So, points scored for 'x' baskets = $2x$

Also, points scored for 'y' baskets = $3y=3(27-x)=81-3x$

Now, total points scored is equal to the sum of 1 point baskets, 2 point baskets and 3 point baskets. Therefore,

$P=19+2x+81-3x\\\\78=100-x\\\\x=100-78\\\\x=22$

Therefore, number of 2 point baskets = 22

Now, number of 3 point baskets = 27 - 22 = 5

So, there were 19 one point baskets, 22 two point baskets and 5 three point baskets.

Answer 2

Answer:

The team made 22 2-point shots and 5 3-point shots.

Step-by-step explanation:

This question can be solved by a system of equations.

I am going to say that:

x is the number of 2 point shots.

y is the number of 3 point shots.

The remaining 27 baskets we're 2 point and 3 point shots

There were 27 shots, so

$x + y = 27$

Allison's team scored 78 points in total. Nineteen of the baskets counted 1 point each.

So all the remaining shots counted for 78 - 19 = 59 points. So

$2x + 3y = 59$

From the other equation, we have that:

$y = 27 - x$

So

$2x + 3(27 - x) = 59$

$2x + 81 - 3x = 59$

$x = 22$

$y = 27 - x = 27 - 22 = 5$

The team made 22 2-point shots and 5 3-point shots.