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3 years ago

Best Deal 1

Mathematics

1 answer:

scoray [572]3 years ago

8 0

Answer:

C) 18 cents

Step-by-step explanation:

Given,

This weeks deal -

Quantity of Flour Price ($) Price per pound ($)

3 pounds 5.25 (5.25/3) = 1.75

5 pounds 9.75 (9.75/3) = 1.95

7 pounds 12.60 (12.60/3) = 1.80

10 pounds 14.20 (14.20/3) = 1.42

12 pounds 18.24 (18.24/3) = 1.52

The lowest price per pound is $1.42. Therefore, this is the current week's best deal.

The last week's best deal was = $`1.60/pound

The difference between the unit price for previous week's best deal and this week's best deal = $1.60 - $1.42 = $0.18

Therefore, 18 cents.

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Rectangle LMNO is similar to rectangle PQRS. What is the length of segment QP?

kherson [118]

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6 0

3 years ago

George is considering two different investment options. The first option offers 7.4% per year simple interest on the

jok3333 [9.3K]

Answer:

Part A: The value of the simple interest investment at the end of three years is $12,220

Part B: The value of the compounded quarterly interest investment at the end of three years is $12,134.08

Part C: The simple interest investment is better over the first three years

Part D: I advise George to invest his money in the compounded interest investment if he will keep the money for a long time

Step-by-step explanation:

Part A:

A = P + P r t, where

A represents the value of the investment
P represents the original amount
r represents the rate in decimal
t represents the time in years

∵ George deposits $10,000

∴ P = 10,000

∵ First option offers 7.4% per year simple interest

∴ r = 7.4% = 7.4 ÷ 100 = 0.074

∵ He may not withdraw any of the money for three years after

the initial deposit

∴ t = 3

- Substitute all of these values in the formula above

∴ A = 10,000 + 10,000(0.074)(3)

∴ A = 10,000 + 2,220

∴ A = 12,220

The value of the simple interest investment at the end of three years is $12,220

Part B:

$A=P(1+\frac{r}{n})^{nt}$ , where

A represents the value of the investment
P represents the original amount
r represents the rate in decimal
n is a number of periods of a year
t represents the time in years

∵ George deposits $10,000

∴ P = 10,000

∵ The second option offers a 6.5% interest rate compounded quarterly

∴ r = 6.5% = 6.5 ÷ 100 = 0.065

∴ n = 4 ⇒ quarterly

∵ He may not withdraw any of the money for three years after

the initial deposit

∴ t = 3

- Substitute all of these values in the formula above

∴ $A=10,000(1+\frac{0.065}{4})^{(4)(3)}$

∴ $A=10,000(1.01625)^{12}$

∴ A = 12,134.08

The value of the compounded quarterly interest investment at the end of three years is $12,134.08

Part C:

∵ 12,220 > 12,134.08

∴ The simplest interest investment is better than the compounded

interest investment at the end of three years

The simple interest investment is better over the first three years

Part D:

I advise George to invest his money in the compounded interest investment if he will keep the money for a long time

Look to the attached graph below

The red line represents the simple interest investment
The blue curve represents the compounded interest investment
(Each 1 unit in the vertical axis represents $1000)
After 0 years and before 4.179 years the red line is over the blue curve, that means the simple interest is better because it gives more money than the compounded interest
After that the blue curve is over the red line that means the compounded quarterly is better because it gives more money than the simple interest