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

Answer:

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

Step-by-step 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) :

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

Answer 2

Answer:

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Step-by-step explanation: