8) the Ratio Of

3 1 8) The ratio of 5to 2 5 10

Solution:

3 5 = 28/5 5

1 2 = 21/10 10

Ratio = 28/5 : 21/10 = 28 : 21/2 = 56 : 21

Divide by 7: Ratio = 8:3

24) The ratio of 7 dimes to 3 quarters.

Solution:

7 dimes = 70 cents

3 quarters = 75 cents

Ratio = 7 dimes : 3 quarters = 70:75 = 14:15 (by dividing by 5) 34) Marc took 3 hours (h) to mow a lawn while Angelina took 150 minutes (min) to mow the same lawn a week earlier. Write the ratio of Marc’s time to Angelina’s time as a ratio of whole numbers.

Solution:

Convert Marc’s time in minutes.

Marc's time = 3 hours = 3 * 60 minutes = 180 minutes

Angelina's time = 150 minutes

Ratio = Marc's time : Angelina's time = 180 : 150 = 6 : 5

14) Find the rate 240 poundsoffertilizer 6lawns

Solution:

6 lawns cost 240 pounds of fertilizer.

1 lawn would cost = 240/6 pounds = 40 pounds

Rate = 40 pounds of fertilizer per lawn.

30) Which is the better buy: 5 lb of sugar for $4.75 or 20 lb of sugar for $19.92?

Solution:

Rate of 5 lb of sugar for $4.75: 4.75/5 = $0.95 per pound

Rate of 20 lb of sugar for $19.92: 19.92/20 = $0.996 per pound

Since $0.95 < $0.996, Thus 5 lb of sugar for $4.75 is a better buy.

10) Write the proportion that is equivalent to the given statement

If Maria hit 8 home runs in 15 softball games, then she should hit 24 home runs in 45 games.

Solution:

Equivalent proportion will be

8/15 = 24/45

28) Determine whether each pair of fractions is proportional

5 75 = 8 120 Solution: Cross multiply:

5*120 = 600

8*75 = 600

Both are equal thus fractions are proportional.

48) Determine if the given rates are equivalent

12gallons 9 gallons = 8,329ft2 1,240 ft 2

Solution:

Cross-multiply:

12*1240 = 14880

9*8329 = 74961

They are different, therefore fractions are not equivalent.

16) A store has T-shirts on sale at 2 for $5.50. At this rate, what do five T-shirts cost?

Solution:

Let x be the cost of five T-shirts. Then proportion will be

5.50 x  2 5 x  $13.75

The cost of five T-shirts is $13.75. Activity Cal/h Activity Cal/h Bicycling 6 mi/h 240 Running 10 mi/h 1,280 Bicycling 12 mi/h 410 Swimming 25 yd/min 275 Cross-country skiing 700 Swimming 50 yd/min 500 Jogging 5 mi/h 740 Tennis (singles) 400 Jogging 7 mi/h 920 Walking 2 mi/h 240 Jumping rope 750 Walking 3 mi/h 320 Running in place 650 Walking 4 mi/h 440

For problems 1 through 4, assume a 150-pound person 1 1 1) If a person jogs at a rate of 5 mi/h for 3 h in a week, how many calories do they 2 2 burn? Solution:

Jogging at that rate burns 740 calories per hour.

Multiply that by 3 ½ = 3.5 hours:

Calories burnt = 740*3.5 = 2590 calories

2) If a person runs in place for 15 minutes, how many calories will be burned?

Solution:

You burn 650 calories an hour.

15 minutes = ¼ of an hour

Calories burnt = ¼ * 650 = 162.5 calories 3) If a person cross-country skis for 35 minutes, how many calories will be burned? Solution:

Calories burnt 700 calories per hour

35 minutes = 35 / 60 hours = 7/12 hours

Calories burnt in 35 minutes = 7/12 * 700 = 408.33 calories

4) How many hours would a person have to jump rope in order to lose 1 pound? (Assume calorie consumption is just enough to maintain weight, with no activity.)

Solution:

Jumping rope is 750 calories per hour.

You need to burn 3500 cals to lose a pound:

2 Number of hours = 3500 / 750 = 4 hours = 4.67 hours 3

Heavier people burn more calories (for the same activity), and lighter people burn fewer. In fact, you can calculate similar figures for burning calories by setting up the appropriate proportion

5) At what rate would a 120-pound person, burn calories while bicycling at 12 mi/h?

A 150 pound person burns 410 cal per hour.

Let x be the rate.

Then proportion will be

150/410 = 120/x Cross multiply:

150x = 120*410

Divide by 150: x = 120*410/150 = 328 cal/hr

6) At what rate would a 180-pound person, burn calories while bicycling at 12 mi/h?

Solution:

Let x be the rate.

Then proportion will be

150/410 = 180/x

Cross multiply:

410*180 = 150x

Divide by 150: x = 410*180/150 x = 492 cal/hr

Rate is 492 cal/hr.

7) How many hours of jogging at 5 mi/h would be needed for a 200-pound person to lose 5 pounds? (Again, assume calorie consumption is just enough to maintain weight, with no activity.) Solution:

A 150 pound person burns 740 cal/hr

Proportion will be

150/740 = 200/x

Cross multiply:

150x = 200*740 x = 740*200/150 x = 986.67 cal/hr

5 pounds * 3500 cal/pound = 17500 calories need to be burned

17500 No. of hours =  17.74 hours 986.67