Algebra Practice Test 1

The following proportion may be written:

\(\frac{1}{p}=\frac{x}{5}\)

Solving for the variable \(x\) gives \(xp = 5\), where \(x=\frac{5}{p}\). So, Lynn can type \(\frac{5}{p}\) pages in five minutes.

Sally can paint \(\frac{1}{4}\) of the house in one hour. John can paint \(\frac{1}{6}\) of the same house in one hour. In order to determine how long it will take them to paint the house, when working together, the following equation may be written:

\(\frac{1}{4}x+\frac{1}{6}x=1\)

Solving for \(x\) gives \(\frac{5}{12}x=1\), where \(x\) is 2.4 hours, which is 2 hours and 24 minutes.

First, apply the 15% sale discount to the original price. Fifteen percent of 450 is 67.50, so the sales price is:

\($450-$67.50=$382.50\)

Next, the employee discount is 20% off the sale price. Twenty percent of 382.50 is 76.50, so the final cost is:

\($382.50-$76.50=$306\)

A 20% discount means you pay 80% of the original price. Let the original price be \(x\):

\(0.8x = $12,590\)

Divide both sides by 0.8 to solve for \(x\):

\(x=\frac{$12,590}{0.8}=$15,737.50\)

In order to solve for \(A\), both sides of the equation may first be multiplied by 3. This is written as \(3 \times \frac{2A}{3}=3(8+4A)\) or \(2A=24+12A\). Subtraction of \(12A\) from both sides of the equation gives \(-10A=24\). Division by -10 gives \(A = -2.4\).

Let Sue’s age be \(s\). Since Leah is 6 years older, Leah’s age is \(s + 6\). John is 5 years older than Leah, so John’s age is \((s + 6) + 5 = s + 11\).

Their total age is \(s + (s + 6) + (s + 11) = 41\).

Combine like terms:

\(3s + 17 = 41\)

Subtract 17:

\(3s = 24\)

Finally, divide by 3:

\(s = 8\)

Simple interest is represented by the formula \(I = Prt\), where \(P\) represents the principal amount, \(r\) represents the interest rate, and \(t\) represents the time.

Substituting $4,000 for \(P\), 0.06 for \(r\), and 5 for \(t\) gives \(I = 4,000 \times 0.06 \times 5\), or \(I = 1,200\). So, he will receive $1,200 in interest.

A 35% profit means the selling price is 135% of the cost. To find the cost, divide the selling price by 1.35:

\(\text{Cost}= \frac{670}{1.35} \approx 496.30\)

The amount of taxes is equal to \($55 \times 0.003\), or $0.165. Rounding to the nearest cent gives 17 cents.

The GPA may be calculated by writing the following expression:

\(\frac{(3\times2)+(4\times3)+(2\times4)+(3\times3)+(4\times1)}{13}\)

This equals 3.0.

From 8:15 a.m. to 4:15 p.m., he gets paid $10 per hour, with the total amount paid represented by the following equation:

\($10 \times 8=$80\)

From 4:15 p.m. to 10:30 p.m., he gets paid $15 per hour, with the total amount paid represented by the following equation:

\($15 \times 6.25=$93.75\)

The sum of $80 and $93.75 is $173.75, so he was paid $173.75 for 14.25 hours of work.

If she removes 13 jelly beans from her pocket, she will have 3 jelly beans left, with each color represented. If she removes only 12 jelly beans, green or blue may not be represented.

The value of \(z\) may be determined by dividing both sides of the equation \(r=5z\) by 5. Doing so gives \(\frac{r}{5}=z\).

Substituting \(\frac{r}{5}\) for the variable \(z\) in the equation \(15z=3y\) gives \(15 \times \frac{r}{5}=3y\).

Solving for \(y\) gives \(r = y\).

50 cents is half of one dollar, thus the ratio is written as half of 300, or 150, to \(x\). The equation representing this situation is:

\(\frac{300}{x}\times \frac{1}{2}=\frac{150}{x}\)

The following proportion may be used to determine how much Lee will make next week:

\(\frac{22}{132}=\frac{15}{x}\)

Solving for \(x\) gives \(x = 90\). Thus, she will make $90 next week if she works 15 hours.

The given equation should be solved for \(x\). Doing so gives \(x = 6\). Substituting the \(x\)-value of 6 into the expression \(5x + 3\) gives \(5(6) + 3\), which is 33.

The amount you will pay for the book may be represented by the expression \(80+(80 \times 0.0825)\). Thus, you will pay $86.60 for the book. The change you will receive is equal to the difference of $100 and $86.60, which is $13.40.

The amount you have paid for the car may be written as \($3,000 + 6($225)\), which equals $4,350.

You will need 40 packs of pens and three sets of staplers. Thus, the total cost may be represented by the expression \(40(2.35) + 3(12.95)\). The total cost is $132.85.

Substituting 3 for \(y\) gives \(33 (33-3)\), which equals \(27(27 – 3)\), or \(27(24)\). Thus, the expression equals 648.