A business analyst uses the linear equation \frac{2}{5}(3p - 10) - 1.2 = 0.4(p + 5) to est… — ACT

A business analyst uses the linear equation $\frac{2}{5}(3p - 10) - 1.2 = 0.4(p + 5)$ to estimate the equilibrium price $p$ , in dollars, of a new product. What is the equilibrium price, in dollars, of the product?

Answer: 9 dollars

Answer

The equilibrium price of the product is

9

dollars.

Converting the fraction to a decimal gives

0.4(3p - 10) - 1.2 = 0.4(p + 5)

. Dividing both sides by

0.4

results in

3p - 10 - 3 = p + 5

, which simplifies to

3p - 13 = p + 5

. Subtracting

p

and adding

13

to both sides gives

2p = 18

, and dividing by

2

results in

9

Step-by-Step Solution

Convert the fraction to decimal form

0.4(3p - 10) - 1.2 = 0.4(p + 5)

Converting

\frac{2}{5}

0.4

makes all terms decimals, simplifying further operations.

Divide both sides of the equation by

0.4

(3p - 10) - 3 = p + 5

Since

0.4

is a common factor and

1.2 / 0.4 = 3

, dividing both sides by

0.4

simplifies the coefficients.

Simplify the left side of the equation

3p - 13 = p + 5

Combine the constant terms

-10

and

-3

to simplify the expression.

Isolate the variable terms on one side

2p = 18

Subtract

p

from both sides and add

13

to both sides.

Solve for

p

p = 9

Divide both sides by

2

to find the final value.

Key Concept

Solving Linear Equations

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic