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How Do You Solve a Word Problem Using a Proportion?

The scale on a blueprint for a house is 2 inches for 5 feet. If the roof is 8.5 inches on the blueprint, what is the actual height of the house?

Summary

  1. 'h' is a variable that represents the actual height of the house
  2. The left side of the proportion is the scale of the blueprint
  3. The scale is 2 inches for 5 feet
  4. The right side of the proportion is the house's height on the blueprint, 8.5 inches, over its actual height, h
  5. Cross-multiply to solve for h
  6. Multiply 2•h on the left
  7. Multiply 5•8.5 on the right

Notes

    1. 'h' is a variable that represents the actual height of the house
    1. The height of the house on the blueprint was 8.5 inches
    2. The scale given in the problem is 2 inches for 5 feet
    3. This scale will allow us to set up a proportion to find the actual height of the house
    1. Remember, we represented this with our variable 'h'
    1. The scale lets us know how many inches on the blueprint stand for how many feet on the real house
    2. So 2 inches on the blueprint represent 5 feet of real house
    1. Since we know the height of the house on the blueprint, we can use this scale to find its actual height
    1. We need to set up a proportion
    2. A proportion is two ratios set equal to each other
    1. The length on the blueprint was in the numerator of our first ratio
    2. So the height on the blueprint, 8.5, will go in the numerator of our second ratio
    1. The actual length was in the denominator of our first ratio
    2. So the actual height of the house, h, will go in the denominator of our second ratio
    1. 'h' is a variable that represents the actual height of the house
    1. 'h' is a variable that represents the actual height of the house
    1. 'h' is a variable that represents the actual height of the house
    2. The means-extremes property of proportions says we can cross-multiply to solve a proportion for a variable
    1. 'h' is a variable that represents the actual height of the house
    2. The means-extremes property of proportions says we can cross-multiply to solve a proportion for a variable
    3. So multiply the extremes, 2 and h, to get the left hand side of the equation
    1. The means-extremes property of proportions says we can cross-multiply to solve a proportion for a variable
    2. So multiply the means, 5 and 8.5, to get the right hand side of the equation
    1. Multiply 5•8.5 on the right hand side to get 42.5
    1. 'h' is a variable that represents the actual height of the house
    2. On the left hand side, the 2's cancel to leave us with h
    3. On the right hand side, divide 42.5 by 2 to get 21.25