Download Ratio and Proportion problems-2

Ratio and Proportion – 2
1. A photograph 6 inches wide and 7 inches high must be reduced to fit in a space 4½
inches wide. How much vertical space will the reduced version require??
6:7 = 4.5:x
x = 5.25
2.
3. When constructing a roadway, the civil engineer must set a stake where the outer
slope of an embankment will meet the ground. This tells the equipment operator
where to begin the embankment. The drawing below shows a 40-foot roadway and the
right and left embankments. Using the indicated measurements, find the distances X
and Y. Note that the two sides of the embankment do not have the same height.
X = 20 + 10 × 1.5/1 = 20 + 15 = 35
Y = 20 + 12 × 2/1 = 20 + 24 = 44
4. The ratio of total sales to average inventory is called an "inventory ratio.'' This ratio
tells a retail store manager the number of times her inventory will turn over in a year.
By dividing this ratio into 365, she determines how often she needs to restock. Find
the inventory ratio for an appliance store with total sales of $495,000 and an average
inventory of $132,000. Then compute the amount of time each inventory lasts?
inventory ratio = $495,000/$132,000 = 3.75
365 / 3.75 ≈ 97 days
5. Five people invest $67,000 in an apartment building in the following amounts:
A-$8,000; B-$18,000; C-$13,000; D-$21,000; E-$7,000
If the distribution of cash flow is proportional to the amounts invested, how much will each
partner receive out of a $475 total monthly cash flow? ·
Total investment = $8,000 + $18,000 + $13,000 + $21,000 + $7,000 = $67,000
A: 475 × 8000/67000 = 56.72
C: 475 × 13000/67000 = 92.2
E: 475 × 7000/67000 = 49.63
B: 475 × 18000/67000 = 127.6
D: 475 × 21000/67000 = 138.9
6. The current in a simple electrical circuit is inversely proportional to the resistance. If
the current is 80 amps when the resistance is 50 ohms, find the current when the
resistance is 40 ohms.
(80 × 50) = 40 × I
=> I = (80 × 50) / 40 = 100
7. A road must be designed that will travel 4 miles horizontally and drop 2500 feet in
elevation. What is the slope of the road as a ratio of horizontal to vertical? (Be sure the
units within the ratio match – 1 mile = 5280 feet, and round to the nearest tenth.)
(4 × 5280):2500 = 8.448:1 ≈ 8.4:1
8. The doctor orders 1/250 grain for a patient. The nurse has a vial labeled 1/200 grain
per cc. If there are 15 minims per cc, how many minims should he give?
(a) (1/250):x = (1/200):15
x = 12
(b) 1/250 grain × (1 cc/ 1/200 grain) × (15 minims / 1 cc) = 12 minims
9. A doctor orders 20 grains of medicine for a patient. The medicine on hand is in tablets
of 250 milligrams each. Given that there are 60 milligrams in 1 grain, how many tablets
does the nurse administer?
(20 × 60):x = 250:1
10. A chemical must be mixed in the ratio of 1 part chemical to 7 parts water. How many
ounces of the chemical should be used to obtain a 2-quart mixture?
1 quart = 32 oz.
1:(1+7) = x:(32×2) 1:8 = x:64
x = 8 oz
11. One of the quantitative measures of the strength of a stock is the ratio of its selling
price to its earnings per share (price-earnings or PE ratio). A stock with good growth
potential will have a high PE ratio, while a troubled stock will have a low PE ratio.
a. Rounded off to the nearest whole number, what is the PE ratio of a stock selling at
$87⅛ and earning $6.36 per share?
87⅛ ÷ 6.36 = 13.7
b. A cosmetics firm has just announced annual earnings of $3.46 per share. Other
cosmetics stocks are selling at an average PE ratio of 9 to 1. Using the same ratio, what
is the potential selling price of this stock? (Round to the nearest dollar.)
3.46 × 9 = 31.14 ≈ 31
12. A certain mix of concrete is composed of 94 lb (one sack) of cement, 50 lb of water,
191 lb of sand, and 299 lb of gravel. The final mix of concrete will weigh 151.2 lb/ft 3•
How many sacks of cement will be needed for a wall with a volume of 1760 ft3?
1760 ft3 × 151.2 lb/ft3 = 266112 lb.
Total weight = 94 + 50 + 191 + 299 = 634
Ratio of cement to concrete = 94:634
Total cement = 266112 × 94/634 = 39455 lb
39455 ÷ 94 = 419.7 => 420 sacks