ACT Preparation / Unit 7 ACT 0623 worked example, 60 to 90 seconds
Solving a Proportion With Units
The idea
To solve a proportion word problem, work in four steps. First, identify the two quantities that stay in a fixed ratio. Second, convert so each quantity uses one unit throughout. Third, write the proportion with the same quantity on top on both sides. Fourth, cross-multiply, solve, and check that the answer has the units the question asks for.
In practice
Worked example: a recipe uses 3 cups of flour for 24 cookies. How many cups make 5 dozen? Step two: 5 dozen is 60 cookies. Step three: 3/24 = x/60. Step four: 24x = 180, so x = 7.5 cups. Second: on a map, 2 inches represent 15 miles. A road of 52.5 miles: 2/15 = x/52.5, so 15x = 105, and x = 7 inches.
Where people slip
The unit conversion is where the error hides: leaving 5 dozen as 5 gives 0.625 cups. Convert before setting up the proportion.
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