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.

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