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Ultimate Math Quiz:

Jim weighs 30 pounds less than Tom, and together they weigh 210 pounds. Let n = Tom's weight in pounds.

A class of 19 pupils has five more girls than boys. Let n = the number of boys.

Two sides of a triangle are equal in length and double the length of the shortest side. The perimeter of the triangle is 36 inches.

Answer :

mariangel
1. Let n = Tom's weight in pounds.
m=Jim's weight in pounds.

m=n - 30
m+n=210

We solve this by substitution:
(n - 30)+n=210
2n-30=210
2n=210+30
2n=240
n=120 pounds weighs Tom
m=120-30=90 pounds weighs Jim


2. Let n = the number of boys.
g = the number of girls.

n+g=19
g=n+5

By substitution:
n+(n+5)=19
2n+5=19
2n=19-5
2n=14
n=14:2
n=7 boys
g=7+5=12 girls

3. Let n = the shortest side of the triangle
each of the two sides that are equal in length=2n

The perimeter=n+2n+2n=36 inches
5n=36
n=7.2 inches is the shortest side of the triangle
2*7.2=14.4 inches is each of the two sides that are equal in length

Answer: . Let n = Tom's weight in pounds.

m=Jim's weight in pounds.

m=n - 30

m+n=210

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