A history teacher is writing a test worth 100 points. She uses multiple-choice questions worth 6 points each and true/false questions worth 2 points each. She wants the test to have three times as many multiple-choice questions as true/false questions. Let m represent the number of multiple-choice questions on the test, and let t represent the number of true/false questions. Which system of equations can be used to find how many of each type of question she should write.

6m + 2t = 100

AND

m=3t

solution t=5 m=15

Step-by-step explanation:

6m + 2t = 100 as each m question gives 6 points and each t question gives 2

m=3t as m questions are 3 times t questions

answer: 0+0=0

step-by-step explanation:

that is the only answer that can make 0

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .