Area and Algebra Word Problems

This lesson covers interpreting fractions, solving equations, and applying mathematical concepts to real-world problems. It includes exercises on identifying equivalent expressions, solving equations using diagrams, creating story problems, calculating paint mixtures, and comparing triangle areas.

Which of the following expressions is equivalent to 3.15 divided by 0.45?

• 3.15 minus 0.45

• 3.15 times 45

• 3.15 plus 0.45

• 3.15 times 1/0.45

What is the solution to the equation 3/4x = 15?

• x = 15

• x = 10

• x = 5

• x = 20

If 4x equals 32, what is the value of x?

• x = 32

• x = 16

• x = 4

• x = 8

In the equation 4 = 32x, what does x equal?

• x = 1/8

• x = 1/4

• x = 8

• x = 4

What is the value of x in the equation 10x = 26?

• x = 3

• x = 2

• x = 2.6

• x = 2.5

How would you represent the equation 3/4 + x = 2 in a story problem?

• Three-fourths of a mile plus the distance to a store equals two miles.

• Three-fourths of a book plus the number of pages equals two books.

• Three-fourths of a pizza plus the price of a drink equals two pizzas.

• Three-fourths of a dollar plus the price of a drink equals two dollars.

In a paint mixture, if 40% is white and 20% is blue, how many cups of white paint are used if there are 4 cups of blue paint?

• 4 cups

• 6 cups

• 8 cups

• 10 cups

How many cups of red paint are used if 40% of the mixture is white and 20% is blue?

• 12 cups

• 16 cups

• 8 cups

• 4 cups

What is the total yield of the lilac paint mixture if it consists of 4 cups of blue, 8 cups of white, and 8 cups of red paint?

• 28 cups

• 24 cups

• 20 cups

• 16 cups

Which triangle has a greater area: Triangle P with a base of 12 inches and height of 8 inches, or Triangle Q with a base of 15 inches and height of 6.5 inches?

• Cannot be determined

• Triangle P

• Triangle Q

• Both have the same area