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3 years ago

How to solve this problem: 1 1/2(n-4 1/2)=12

Mathematics

1 answer:

Vikentia [17]3 years ago

4 0

Answer:

n = 25/2, or n = 12 1/2

Step-by-step explanation:

It's essential that you use parentheses here to show how your numerals are grouped. I have made some assumptions here, and believe you meant:

(1 1/2)(n - 4 1/2) = 12.

First, convert 1 1/2 and 4 1/2 into improper fractions:

(3/2)(n - 9/2) = 12

Multiplying both sides by (2/3) eliminates the fractional coefficient (3/2):

n - 9/2 = (2/3)(12), or n - 9/2 = 8.

Again, eliminate the fraction by multiplying all terms by 2:

2n - 9 = 16

Then 2n = 25, and n = 25/2, or n = 12 1/2

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Answer:

(A) The rate of change in the price of a bushel of corn in the current year is $7.

(B) The price of a bushel of corn in the current year is $2 more than the price of a bushel of corn in the previous year.

Step-by-step explanation:

The graph for the prices of different numbers of bushels of corn at a store in the current year is shown below.

Part A:

The rate of change in the price of a bushel of corn in the current year based upon the number of bushels is known as the slope of the line.

The formula to compute the slope is:

$\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Consider the ordered pairs: (4, 28) and (10, 70)

Compute the slope of the line as follows:

$\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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Thus, the rate of change in the price of a bushel of corn in the current year is $7.

Part B:

The data for the price of bushels in the previous year is as follows:

Number of Bushels Price

2 10

4 20

6 30

8 40

Compute the rate of change in the price of a bushel of corn in the previous year based upon the number of bushels as follows:

Consider the ordered pairs: (2, 10) and (6, 30)

$\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$=\frac{30-10}{6-2}\\\\=\frac{20}{4}\\\\=5$

The rate of change in the price of a bushel of corn in the previous year is $5.

Thus, the price of a bushel of corn in the current year is $2 more than the price of a bushel of corn in the previous year.

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3 years ago