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,
[tex]X.1+Y.2+Z.3=74[/tex] (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 :
[tex]Y=Z+2\\Z=X+2[/tex]
Let's write Y and X in terms of Z
[tex]Y=Z+2[/tex] (II)
[tex]Z=X+2[/tex] ⇒ [tex]X=Z-2[/tex] (III)
Replacing (II) and (III) in (I) :
[tex](Z-2).1+(Z+2).2+Z.3=74[/tex]
[tex]Z-2+2Z+4+3Z=74[/tex]
[tex]6Z+2=74\\6Z=72\\Z=12[/tex]
We find that the variable Z is 12. Replacing this value in (II) and (III) ⇒
[tex]Y=12+2=14\\Y=14[/tex]
[tex]X=12-2=10\\X=10[/tex]
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) :
[tex]10.1+14.2+12.3=74\\10+28+36=74\\74=74[/tex]
Answer:
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Step-by-step explanation:
