Macario knows that he has scored a total of 70 points so far this basketball season. His coach told him that he has scored 37 times, but Macario wants to know how many free throws, field goals, and three pointers he has made. The sum of his field goals and three pointers equal twice the number of free throws minus two. How many free throws, field goals, and three pointers has Macario made?

Question

anonymous · Answer

it cool

fortytherapper · Answer

I'll set up the system of equations, and you take it from there?

X = Free Throws
Y = Field Goals
Z = Three Pointers

X + Y + Z = 37
X + 2Y + 3Z = 70

Hint: Like numbers, you can also add, subtract, multiply, and divide equations with one another

jdoe0001 · Answer

a = singles
b = doubles
c= triples

so, we know he has scored 37 times
thus $\bf a+b+c=37$
we also know that the sum of doubles and triples is twice as singles -2
or $\bf b + c = 2a -2$
thus $\bf  a+{\color{brown}{  b+c}}=37
\ \quad \
{\color{brown}{  b+c}}=2a-2
$
do some substitution there, and find "a" first off

jdoe0001 · Answer

once you found "a"
substitute in a + b + c = 37
to find $\bf b+c$
once you found b + c
use that, to substitute on $\bf b+c=a-2$

jdoe0001 · Answer

$\bf b+c=2a-2$  rather