Page 160 - ArithBook5thEd ~ BCC

Example 201. A runner burns 375 calories running 3.5 miles. (a) How many calories will she burn in
running a marathon (approximately 26 miles)? (b) What is her rate of energy use (calories per mile)?
Round off to the nearest whole unit.

Solution. (a) The ratio
calories
miles
is assumed fixed and, from the given information, is equal to
375
.
3.5

Let x denote the number of calories the runner burns in running a marathon. Then
375 x calories
= (setting cross-products equal)
3.5 26 miles
(375)(26) = 3.5x
(375)(26)
x = ≈ 2786.
3.5
She will burn approximately 2786 calories running the marathon. (b) Her rate of energy use is

375 calories
≈ 107 calories per mile.
3.5 miles

Example 202. A painting crew can paint three apartments in a week. If a buildingcontains 40 equal
size apartments, how long will it take the crew to paint all the apartments?

Solution. The ratio
apartments painted
time in weeks
3
is given as .If y is the number of weeks needed to paint 40 apartments, then
1
3 40
= ,
1 y
1
and y = 40 =13 weeks.
3 3
5.4.1 Exercises

Use proportions to solve the following problems.
1. On a map, 3 inch represents 14 miles. If two cities are 42 miles apart, how far apart are they on
4
the map?

1
2. A truck burns 2 quarts of oil on an 1800 mile trip. How many quarts will be burned on a cross-
2
country trip of 3240 miles?
3. An investment of $2, 000 earns $48 in interest over a year. How much would need to be invested
to earn $200 in interest? (Round to the nearest dollar.)

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