Question

On March 9, 2018, NCAA fans across the world were shocked when the Retrievers of the University of Maryland, Baltimore County (UMBC) upset the Virginia Cavaliers. UMBC scored a total of 74 points resulting from a combination of 3-point baskets, 2-point baskets, and 1-point free throws. There were 2 more 2-point baskets than 3-point baskets and 2 more 3-point baskets than 1-point free throws.

a) Set up a system of linear equations to find the number of three-point baskets, two-point baskets, and one-point free-throws. (label your variables)

Answer 1

plz dont delete answer but i need one more answer to complete challenge so plz dont delete or report thx

Explanation:

Answer 2

UMBC scored 10,14 and 12 one - point free throws, two point baskets and three point baskets respectively.

Explanation:

Let's start defining the variables.

X : ''Number of 1 - point free throws''

Y : ''Number of 2 - point baskets''

Z : ''Number of 3 - point baskets''

UMBC scored a total of 74 points. Therefore,

`X.1+Y.2+Z.3=74` (I)

Where X.1 represents the total points from 1 - point free throws.

Where Y.2 represents the total points from 2 - point baskets.

And finally Z.3 represents the total points from 3 - point baskets.

Reading the exercise, we can write two more equations :

`Y=Z+2\\Z=X+2`

Let's write Y and X in terms of Z

`Y=Z+2` (II)

`Z=X+2` ⇒
`X=Z-2` (III)

Replacing (II) and (III) in (I) :

`(Z-2).1+(Z+2).2+Z.3=74`

`Z-2+2Z+4+3Z=74`

`6Z+2=74\\6Z=72\\Z=12`

We find that the variable Z is 12. Replacing this value in (II) and (III) ⇒

`Y=12+2=14\\Y=14`

`X=12-2=10\\X=10`

Finally, UMBC scored 10 baskets from 1 - point free throws,14 baskets from of 2 - point and 12 baskets of 3 - point.

We can verify by replacing X = 10 , Y = 14 and Z = 12 in equation (I) :

`10.1+14.2+12.3=74\\10+28+36=74\\74=74`