New SAT Math Workbook

Whenever two quantities vary directly a problem can

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Unformatted text preview: . Whenever two quantities vary directly, a problem can be solved using a proportion. We must be very careful to compare quantities in the same order and in terms of the same units in both fractions. If we compare miles with hours in the first fraction, we must compare miles with hours in the second fraction. You must always be sure that as one quantity increases or decreases, the other changes in the same direction before you try to solve using a proportion. Example: If 4 bottles of milk cost $2, how many bottles of milk can you buy for $8? Solution: The more milk you buy, the more it will cost. This is direct. We are comparing the number of bottles with cost. 4x = 28 If we cross multiply, we get 2x = 32 or x = 16. A shortcut in the above example would be to observe what change takes place in the denominator and apply the same change to the numerator. The denominator of the left fraction was multiplied by 4 to give the denominator of the right fraction. Therefore we multiply the numerator by 4 as well to maintain the equality. This method often means a proportion can be solved at sight with no written computation at all, saving valuable time. Example: If b boys can deliver n newspapers in one hour, how many newspapers can c boys deliver in the same time? Solution: The more boys, the more papers will be delivered. This is direct. We are comparing the number of boys with the number of newspapers. bc Cross multiply and solve for x. = nx bx = cn cn x= b 58 Chapter 4 Exercise 2 Work out each problem. Circle the letter that appears before your answer. 1. Find the cost, in cents, of 8 books if 3 books of the same kind cost D dollars. (A) 8D 3 3 (B) 800 D 3 (C) 8D 800 D (D) 3 108 D (E) 3 1 On a map inch = 10 miles. How many miles 2 1 4. Mark’s car uses 20 gallons of gas to drive 425 miles. At this rate, approximately how many gallons of gas will he need for a trip of 1000 miles? (A) 44 (B) 45 (C) 46 (D) 47 (E) 49 If r planes can carry p passengers, how many planes are needed to carry m passengers? (A...
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