Question

Use the following information below to answer the next 2 questions. Between 1980 and 2000, the cost of a gallon increased by 30%. In 1980, the cost of a gallon of milk was $2.16. 1. What was the cost of a gallon of milk in 1990? 2. What was the cost of a gallon of milk in 1997?

Answer 1

EXPLANATION

The increasing relationship is given by the following expression:

`\text{Increasing = 100}\cdot((final-inicial))/(inicial)`

In this case, as the incresing over 20 years was of 30%, for 10 years the increasing would be 15%, so replacing terms:

`15=100\cdot(final-2.16)/(2.16)`

Multiplying both sides by 2.16/100:

`(2.16\cdot15)/(100)=final-2.16`

Adding 2.16 to both sides:

`Final_{\text{price}}=(2.16\cdot15)/(100)+16`

Simpifying:

`\text{Final}_{\text{price}}=(81)/(250)+16`

Adding numbers:

`\text{Final}_{\text{price}}=0.324+16=16.324`

The price in 1990 was $16.324

2) To calculate the price in 1997, we need to calculate the increasing rate by year, and then multiply this number by the amount of years as shown as follows:

`\text{Increasing rate}_{by\text{ year}}=\frac{30}{20\text{ years}}=1.5/\text{year}`

Then, multiplying 1.5 by 1997-1980=17 years give us the following increasing:

1.5 * 17 = 25.5%

Now, substituting 25.5 on the increasing formula:

`25.5=100\cdot((final-2.16))/(2.16)`

Multiplying both sides by 2.16/100:

`(25.5\cdot2.16)/(100)=\text{final}-2.16`

Adding +2.16 to both sides:

`(1377)/(2500)+2.16=\text{final}`

Adding numbers:

`0.5508+2.16=\text{final}`

Adding numbers:

`2.7108=\text{final}`

Switching sides:

`final_(price)=\text{ 2.7108}`

The cost in 1997 was $2.7108