[ratio and proportion word problems][section 50]

(1.)  A train travelled 90 miles in 1.5 hours.   How many miles

will it travel in 6 hours going at the same rate of speed?

90/1.5 = x/6              here is the problem

1.5x = 540              cross multiply
____  ____
1.5   1.5          divide each side by 1.5

x  = 360        divide and cancel

result:   360 miles

(2.)  Fifty feet of copper wire weighs 2 pounds.  How much will

325 feet of the same wire weigh?

50/2 = 325/x               here is the problem

50x = 650           cross multiply
____  ____
50    50           divide each side by 50

x = 13            divide and cancel

result:  13 pounds

(3.)  A recipe for a two-pound cake calls for 1.5 cups of

butter.  How many cups of butter will be needed for

a five-pound cake?

2/1.5 = 5/x          here is the problem

2x = 7.5            cross multiply
___  _____
2     2          divide each side by 2

x = 3.75          divide and cancel

result: 3.75 cups of butter

(4.)  0.7 cm of rain fell in 3 hours.  How many cm of rain

will fall in 9 hours at the same rate?

0.7/3 = x/9               here is the problem

3x = 6.3             cross multiply
____  ____
3     3       divide each side by 3

x = 2.1         divide and cancel

result:  2.1 cm of rain

(5.)   1.5 cm represents 60 km.   What distance does 6 cm

represent?

1.5/60 = 6/x             here is the problem

1.5x = 360        cross multiply
____  _____
1.5    1.5       divide each side by 1.5

x = 240           divide and cancel

result:  240 km

(6.)   5 pounds of meat makes 22 meat patties.   How many

patties of the same size can be made from 17.5 pounds

of meat?

5/22 = 17.5/x            here is the problem

5x = 385              cross multiply
___  ____
5     5         divide each side by 5

x = 77        divide and cancel

result:  77 patties

(7.)  Wallpaper to cover 55 square feet costs \$16.  How much

will it cost to cover 330 square feet?

55/16 = 330/x             here is the problem

55x = 5280              cross multiply
_____  ____
55     55              divide each side by 55

x = 96             divide and cancel

result:  \$96

(8.)   A nurse checking the heartbeat of a patient counted 19

beats in 15 seconds.  What was the patients heartbeat

for 60 seconds?

19/15 = x/60          here is the problem

15x = 1140           cross multiply
____ _____
15    15       divide each side by 15

x = 76         divide and cancel

result:  76 beats per minute

(9.)  A car travels 110 km in 3 hrs.  How far will it travel

in 5 hrs at the same rate of speed?

110/3 = x/5               here is the problem

3x = 550           cross multiply
___ ____
3   3         divide each side by 3

x = 183 1/3       divide and cancel

result:  183 1/3 km

(10.)  A printing press runs 500 copies of a brochure in 8

minutes.  How long will it take to run 200,000 copies

at the same rate?

500/8 = 200,000/x       here is the problem

500x = 1,600,000   cross multiply
______ ___________
500       500       divide each side by 500

x = 3200           divide and cancel

result:  3200 minutes