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7-1 Ratios and Proportions
1. PETS Out of a survey of 1000 households, 460 had at least one dog or cat as a pet. What is the ratio of pet owners
to households?
SOLUTION: The ratio of per owners to households is 23:50.
3. The ratio of the measures of three sides of a triangle is 2:5:4, and its perimeter is 165 units. Find the measure of each
side of the triangle.
SOLUTION: Just as the ratio
or 2:5 is equivalent to
or 2x:5x , the extended ratio can be written as 2x:5x:4x. The perimeter is 165 units, so the sum of the lengths of the sides is 165. Solve for x.
So the measures of the three sides are 2(15) or 30, 5(15) or 75, and 4(15) or 60.
Solve each proportion.
5. SOLUTION: Cross multiply.
Solve for x.
48 = 3x
x = 16
7. SOLUTION: Cross multiply.
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Solve for x.
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Solve for x.
48 = 3x
7-1 Ratios
x = 16and Proportions
7. SOLUTION: Cross multiply.
Solve for x.
9. CCSS MODELING Ella is baking apple muffins for the Student Council bake sale. The recipe that she is using
calls for 2 eggs per dozen muffins, and she needs to make 108 muffins. How many eggs will she need?
SOLUTION: Let the unknown number be x.
Form a proportion for the given information.
Cross multiply.
Solve for x.
MOVIES For Exercises 10 and 11, refer to the graphic below.
11. Which film listed had the lowest ratio of awards to nominations?
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SOLUTION: Page 2
Solve for x.
7-1 Ratios and Proportions
MOVIES For Exercises 10 and 11, refer to the graphic below.
11. Which film listed had the lowest ratio of awards to nominations?
SOLUTION: We can write them in decimal form and then compare their values on the same scale:
Movie A has the lowest ratio, that is, 1:2.
13. The ratio of the measures of the three sides of a triangle is 9: 7: 5. Its perimeter is 191.1 inches. Find the measure of
each side
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SOLUTION: Just as the ratio
or 9:7 is equivalent to
or 9x:7x , the extended ratio can be written as 9x:7x:5x. 7-1 Ratios
Movie and
A hasProportions
the lowest ratio, that is, 1:2.
13. The ratio of the measures of the three sides of a triangle is 9: 7: 5. Its perimeter is 191.1 inches. Find the measure of
each side
SOLUTION: Just as the ratio
or 9:7 is equivalent to
or 9x:7x , the extended ratio can be written as 9x:7x:5x. The perimeter is 191.1 inches so the sum of the lengths of the sides is 191.1. Solve for x. So the measures of the three sides are 9(9.1) or 81.9 in., 7(9.1) or 63.7 in., and 5(9.1) or 45.5 in..
15. The ratio of the measures of the three sides of a triangle is
Its perimeter is 4.75 feet. Find the length of the longest side.
SOLUTION: The given ratio
is equivalent to
The perimeter is 4.75 feet, so the sum of the lengths of the sides is 4.75. Solve for x.
So the measures of the three sides are
or 2.2 ft,
or 1.1 ft, and
or 1.47 ft. The length of the longest side is
2.2 ft.
Find the measures of the angles of each triangle.
17. The ratio of the measures of the three angles is 3:6:1.
SOLUTION: Just as the ratio
or 3:6 is equivalent to
or 3x:6x , the extended ratio can be written as 3x:6x:1x. We know that sum of the measures of all interior angles in a triangle is 180 degrees. Set the sum of the extended
ratios equal to 180 and solve for x. So the measures of the three angles are 3(18) or 54, 6(18) or 108, and 1(18) or 18.
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ratio of- Powered
the measures
of the
19. The Manual
SOLUTION: three angles is 10:8:6.
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7-1 Ratios
and Proportions
So the measures
of the three angles are 3(18) or 54, 6(18) or 108, and 1(18) or 18.
19. The ratio of the measures of the three angles is 10:8:6.
SOLUTION: Just as the ratio
or 10:8 is equivalent to
or 10x:8x , the extended ratio can be written as 10x:8x:6x. We know that sum of the measures of all interior angles in a triangle is 180. Set the sum of the extended ratio equal
to 180 and solve for x.
So the measures of the three angles are 10(7.5) or 75, 8(7.5) or 60, and 6(7.5) or 45.
Solve each proportion.
21. SOLUTION: Cross multiply.
Solve for y.
23. SOLUTION: Cross multiply.
Solve for x.
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25. Page 5
7-1 Ratios and Proportions
23. SOLUTION: Cross multiply.
Solve for x.
25. SOLUTION: Cross multiply.
Solve for x.
27. SOLUTION: Cross multiply.
Solve for x.
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29. NUTRITION According to a recent study, 7 out of every 500 Americans aged 13 to 17 years are vegetarian. In a
7-1 Ratios and Proportions
27. SOLUTION: Cross multiply.
Solve for x.
29. NUTRITION According to a recent study, 7 out of every 500 Americans aged 13 to 17 years are vegetarian. In a
group of 350 13- to 17-year-olds, about how many would you expect to be vegetarian?
SOLUTION: Let the unknown number be x.
Form a proportion for the given information.
Cross multiply.
Solve for x.
ALGEBRA Solve each proportion. Round to the nearest tenth.
31. SOLUTION: eSolutions Manual - Powered by Cognero
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Solve for x.
7-1 Ratios and Proportions
ALGEBRA Solve each proportion. Round to the nearest tenth.
31. SOLUTION: 33. SOLUTION: Use the quadratic formula.
a = 9, b = –114, c = –24
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7-1 Ratios
and Proportions
33. SOLUTION: Use the quadratic formula.
a = 9, b = –114, c = –24
35. The perimeter of a rectangle is 220 inches. The ratio of its length to its width is 7: 3. Find the area of the rectangle.
SOLUTION: The ratio
or 5:2 is equivalent to
or 7x:3x . The perimeter is 220 feet, so the sum of the lengths of the sides is 220. Solve for x.
So the length and width of the rectangle are 7(11) or 77 in. and 3(11) or 33 in. respectively.
Thus the area of the rectangle is 2541 square inches.
37. The ratio of the measures of the angles of a quadrilateral is 2:4:6:3. Find the measures of the angles of the
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quadrilateral.
SOLUTION: Page 9
7-1 Ratios and Proportions
Thus the area of the rectangle is 2541 square inches.
37. The ratio of the measures of the angles of a quadrilateral is 2:4:6:3. Find the measures of the angles of the
quadrilateral.
SOLUTION: Just as the ratio
or 2:4 is equivalent to
or 2x:4x , the extended ratio can be written as 2x:4x:6x:3x. The sum of the measures of all interior angles in a quadrilateral is 360.Set the sum of the extended ratio equal to 360
and solve for x. So the measures of the four angles are 2(24) or 48, 4(24) or 96, 6(24) or 144, and 3(24) or 72.
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