If Billy buys 10 goats, he will have donated 2 goats.

If Billy buys 20 goats, he will have donated 4 goats.

We can set up the equation by finding the slope of the two points \(\displaystyle (10,2)\) and \(\displaystyle (20,4)\).

\(\displaystyle m= \frac{4-2}{20-10} = \frac{2}{10} = \frac{1}{5}\)

Write the slope-intercept equation.

\(\displaystyle y=mx+b\)

Substitute the known slope and a given point.

\(\displaystyle 4=(\frac{1}{5})(20)+b\)

\(\displaystyle b=0\)

Write the equation.

\(\displaystyle y=\frac{1}{5}x\)

Rewrite the equation in terms of \(\displaystyle G\) and \(\displaystyle T\).  The total will be the dependent variable.

The correct answer is:  \(\displaystyle T=\frac{1}{5}G\)

Split up the sentence into parts.

Twice a number:  \(\displaystyle 2x\)

Five less than twice a number:  \(\displaystyle 2x-5\)

The product of negative two and five less than twice a number:

\(\displaystyle -2(2x-5)\)

Is six: \(\displaystyle =6\)

Combine the terms.

The answer is:  \(\displaystyle -2(2x-5)=6\)

Let \(\displaystyle x\) be the desired minimum score the student needs to achieve on his third exam. If he wants his overall average test score to be \(\displaystyle 90\) or more, the following inequality will express the relationship between each of his scores so far, his desired average score, and \(\displaystyle x\):

\(\displaystyle \frac{88+85+x}{3}\geq90\)

Multiplying both sides of the inequality by \(\displaystyle 3\) yields

\(\displaystyle 88+85+x\geq 270\)

Adding like terms of the left-hand side of the inequality yields

\(\displaystyle 173+x\geq 270\)

Subtracting \(\displaystyle 173\) from both sides of the inequality yields

\(\displaystyle x\geq97\).

Hence, the student needs to achieve a score of at least \(\displaystyle 97\) on his next exam in order to achieve a test average of \(\displaystyle 90\).

Break up the sentence into parts.

Twice a number:  \(\displaystyle 2x\)

The cube root of twice the number:  \(\displaystyle \sqrt[3]{2x}\)

The difference of twice a number and the cube root of twice the number:

\(\displaystyle 2x-\sqrt[3]{2x}\)

Is ten:  \(\displaystyle =10\)

Combine the parts to form the equation.

The answer is:  \(\displaystyle 2x-\sqrt[3]{2x}=10\)

Break up the sentence into parts.  Work the terms of the square root first.

Twice a number:  \(\displaystyle 2x\)

The square root of twice a number:  \(\displaystyle \sqrt{2x}\)

Three times the square root of twice a number:  \(\displaystyle 3\sqrt{2x}\)

Is forty:  \(\displaystyle =40\)

Combine the terms to set up the equation.

The answer is:  \(\displaystyle 3\sqrt{2x}=40\)

Break up the sentence into parts.

Eight times a number:  \(\displaystyle 8x\)

Five less than eight times a number:  \(\displaystyle 8x-5\)

Is fourteen:  \(\displaystyle =14\)

The answer is:  \(\displaystyle 8x-5=14\)

Determine how much Billy will earn per day.  Since he works eight hours a day, multiply the hourly wage with the hours.

\(\displaystyle \$3 \times 8 =\$24\)

He will make 24 dollars a day.

For five days:

\(\displaystyle \$24\times 5 =\$120\)

Billy will make 120 dollars per week.

Set up the equation.

The answer is:  \(\displaystyle T=\$120w\)

Break up the sentence into parts.  Start by the inner quantity.

Three less than twice a number:  \(\displaystyle 2x-3\)

Six times the quantity of three less than twice a number:  \(\displaystyle 6(2x-3)\)

Is eleven:  \(\displaystyle =11\)

Combine the parts to form the equation.

The answer is:  \(\displaystyle 6(2x-3)=11\)

Break up the sentence into parts.

Seven times a number:  \(\displaystyle 7x\)

Four less than seven times a number:  \(\displaystyle 7x-4\)

Is eighty:  \(\displaystyle =80\)

Combine the parts.

The answer is:  \(\displaystyle 7x-4=80\)

Split the sentence into parts.

Twenty times a number:  \(\displaystyle 20x\)

Eight less than twenty times a number:  \(\displaystyle 20x-8\)

Is nine:  \(\displaystyle =9\)

Combine the terms.

The equation is:  \(\displaystyle 20x-8=9\)