Question 1

Express the following ratio in its lowest terms. 76: 44: 8

Accepted Answer

The greatest common divisor (GCD) of 76, 44, and 8 is 4. Dividing each term by 4 gives us 19:11:2, which is in its lowest terms.

Question 2

Sam is going to ask for a raise. Over the past year, the CPI has gone from 129.9 to 131.9. Sam currently earns $42,500. What is the minimum raise that Sam should ask for in order to maintain the same buying power?

Accepted Answer

To maintain the same buying power, Sam needs to adjust his salary based on the increase in the Consumer Price Index (CPI). The CPI went from 129.9 to 131.9, which is an increase of 2 points. To find the percentage increase: (131.9 - 129.9) / 129.9 = 0.01539, or 1.539%. To maintain the same buying power, Sam's salary needs to be increased by 1.539% of $42,500, which is $654.075. Adding this to his current salary gives $42,500 + $654.075 = $43,154.075, which rounds to $43,154.

Question 3

The basket of goods and services included in the Consumer Price Index cost $425 in the base year. If the same basket cost $575 ten years later, what was the CPI on that date?

Accepted Answer

The answer of The basket of goods and services included...

Question 4

Total overhead of $235,000 is allocated according to the proportion of labour hours. Department A used 1830 hours, department B used 1635 hours, and department C used 1760 hours. What amount of overhead should be allocated to department C?

Accepted Answer

The answer of Total overhead of $235,000 is allocated according...

Question 5

Carol bought 25.5 hectares of land for $63,000. If she buys another 80 hectares of land at the same price per hectare as her first purchase, how much must she pay for her second purchase?

Accepted Answer

The answer of Carol bought 25.5 hectares of land for...

Question 6

If the "basket" of goods and services included in the consumer price index (CPI) cost $21,350 in the base year (when the CPI = 100) and currently costs $28,550, what is the current CPI?

Accepted Answer

To find the current CPI, we need to use the formula:
CPI = (Cost of basket in current year / Cost of basket in base year) x 100

Plugging in the given values, we get:
CPI = (28,550 / 21,350) x 100
CPI = 1.3372 x 100
CPI = 133.72

Therefore, the current CPI is 133.72, which corresponds to choice A.

Question 7

The price of a box of chalk has increased from $.89 to $1.39 over a ten-year period. What index number would represent the change in price over the ten-year period?

Accepted Answer

To find the index number representing the change in price, we use the following formula:

Index Number = (New Price / Old Price) x 100

Plugging in the values, we get:

Index Number = (1.39 / 0.89) x 100
Index Number = 156.18

Rounding to one decimal place, we get the answer to be 156.2, which is option B.

Question 8

Express the following ratio in its lowest terms. 130: 290: 60

Accepted Answer

To simplify the ratio, we need to find the greatest common factor (GCF) of the three numbers. The GCF of 130, 290, and 60 is 10. Dividing each number by 10 gives us 13:29:6, which is in its lowest terms. Therefore, the answer is E (13:29:6).

Question 9

Suppose C$1.00 is equivalent to US$0.9672. What $C amount would it cost to purchase US$1565? (Ignore any commission.)

Accepted Answer

To find the amount in Canadian dollars (C$) needed to purchase US$1565, divide the amount in US dollars by the exchange rate: US$1565 / US$0.9672 = C$1,618.07.

Question 10

Nitin earns $15 per hour today. Five years ago he earned $11.75 per hour. During the five-year period the CPI rose from 136.5 to 147.6. Has Nitin's buying power increased or decreased and by how much in current year's dollars?

Accepted Answer

The answer of Nitin earns $15 per hour today. Five...

Question 11

The CPI increased from 125.0 to 132.0 over a three-year period. If a person earned $40,000 at the beginning of the three-year period, how much would they have to earn at the end of the three-year period to maintain the same purchasing power?

Accepted Answer

To maintain the same purchasing power, the person's income needs to increase by the same percentage as the CPI. This can be found using the formula:
(income at end of period) = (income at beginning of period) x (ending CPI / beginning CPI)
Substituting the given values, we get:
(income at end of period) = ($40,000) x (132.0 / 125.0) = $42,240
Therefore, the answer is B.

Question 12

Express the following ratio whose smallest term is 1. 3: 21: 0.75

Accepted Answer

The answer of Express the following ratio whose smallest term...

Question 13

Sally earns $25 per hour today. Seven years ago she earned $20.75 per hour. During the seven-year period the CPI rose from 136.5 to 158.2. Has Sally's buying power increased or decreased and by how much in current year's dollars?

Accepted Answer

The answer of Sally earns $25 per hour today. Seven...

Question 14

If the US$ strengthens by 2% relative to the euro (US$1.00 = €0.746826), what will be the new value for the euro per US$1.00?

Accepted Answer

The answer of If the US$ strengthens by 2% relative...

Question 15

Victoria is going to ask for a raise. Over the past year, the CPI has gone from 119.6 to 122.6. Victoria now earns $45,000. What is the minimum raise that Victoria should ask for in order to maintain the same buying power?

Accepted Answer

The answer of Victoria is going to ask for a...

Question 16

The price of a laser printer dropped from $299.99 to $175. What index number would represent the change in price?

Accepted Answer

To find the index number, we use the formula: (New Price/Old Price) x 100. Plugging in the values, we get ((175/299.99) x 100) ≈ 58.3. Therefore, the index number that represents the change in price is 58.3.

Question 17

The basket of goods and services included in the Consumer Price Index cost $35,750 in the base year. If the same basket cost $43,000 six years later, what was the CPI on that date?

Accepted Answer

To calculate the CPI, we use the formula:
CPI = (cost of basket in current year / cost of basket in base year) x 100

In this problem, the cost of the basket in the base year (six years ago) was $35,750. The cost of the same basket six years later is $43,000. So, plugging these numbers into the formula we get:

CPI = (43,000 / 35,750) x 100
CPI = 120.3

Therefore, the CPI on that date was 120.3.

Question 18

Three partners share the partnership's profit according to the proportion of the business each owns. Ms. A owns 30%, Mr. B owns 25% and Ms. C owns the remainder. What profit would Mr. B receive if Ms. A receives $32,500?

Accepted Answer

First, we need to find out what percentage of the partnership Ms. C owns. 
The combined ownership percentage of Ms. A and Mr. B is: 30% + 25% = 55%. 
This means that Ms. C must own the remaining 45%.

Next, we can use a proportion to calculate Mr. B's share of the profit:

Ms. A's share / Ms. A's ownership percentage = Mr. B's share / Mr. B's ownership percentage

Plugging in the numbers we know:

$32,500 / 30% = Mr. B's share / 25%

Solving for Mr. B's share:

Mr. B's share = ($32,500 / 30%) × 25% = $27,083.33

Therefore, the answer is D.

Question 19

If the US$ weakens by 5% relative to the euro (US$1.00 = €0.746826), what will be the new value for the euro per US$1.00?

Accepted Answer

The answer of If the US$ weakens by 5% relative...

Question 20

The CPI increased from 130.0 to 135.0 over a two-year period. If a person earned $35,000 at the beginning of the two-year period, how much would they have to earn at the end of the two-year period to maintain the same purchasing power?

Accepted Answer

The answer of The CPI increased from 130.0 to 135.0...

Quiz 3: Ratios and Proportions