Mathematics Practice Questions 1

The equation \(x-0.10x-0.15(x-0.10x)=306\) may be used to solve the problem.

Solving for \(x\) gives \(0.90x – 0.15x + 0.015x = 306\), where \(x = 400\).

Thus, the original price was $400.

The equation may be solved by first distributing \(y\) across the expression \(x – 1\) on the left side of the equation. Doing so gives \(xy – y = z\).

Adding \(y\) to both sides of the equation gives \(xy = z + y\).

Finally, division of both sides of the equation by \(y\) gives \(x=(z+y) \div y\) or \(x=\frac{z}{y}+1\).

This problem illustrates the distributive property of multiplication over addition. The factor being distributed may not change.

The measure of the third angle of the triangle is equal to \(180°-(15° + 85°)\), or 80°.

Since there are 32 ounces in 2 pounds (16 ounces = 1 pound), the following proportion may be written like this:

\(\frac{5}{140}=\frac{32}{x}\)

Solving for \(x\) gives \(x = 896\). Thus, there are 896 grams in 2 pounds of meat.

The largest number of children taking swimming lessons in one year was 500 in 1995.

The only decrease in number of children taking swimming lessons was from 1992 to 1993, with a decrease of 200 children.

The average may be written as \(\frac{200+250+400+200+300+500}{6}\), which is approximately 308.

Movement of the decimal point two places to the left gives 0.0593.

The following proportion may be used to solve the problem:

\(\frac{1}{20}=\frac{6.2}{x}\)

Solving for \(x\) gives \(x = 124\), so there are 124 miles between the two towns.

The correct graph should show a line segment between 1 and 4, including the points 1 and 4.

The volume of the tin is 972 in. The volume of each piece of fudge is 27 in.

\(972 \div 27 = 36\)

To solve this, call the brother’s age \(x\) and Sarah’s age \(2x\).

Sarah’s age – Brother’s age = 15

\(2x-x=15\)

\(x=15\)

This tells us that the youngest brother is 15 years old.

Multiplying the numerator and denominator of the given fraction by 5 gives the fraction \(\frac{25}{30}\), which is equivalent.

First, calculate the floor area in square feet.

\(12\text{ ft}\times20\text{ ft}=240\text{ ft}^2\)

Then, convert to square yards

\(\tfrac{240}{9}\approx26.6667\text{ yd}^2\)

Finally, multiply by the price per square yard.

\(26.6667\times8.91\approx237.6\)

Solve the following equation for \(x\):

\(6,000=\frac{1}{2}x\)

Solving for \(x\) gives \(x = 12,000\). Thus, the amount of prize money distributed equaled $12,000.

The distance may be determined by writing and solving the following equation for \(c\).

\(50^2+1,20^2=c^2\)

Because \(c = 130\), the distance is 130 feet.

Because the cyclist spends different amounts of time at each speed, you need to use the following formula:

\(\text{average speed}=\frac{\text{total distance}}{\text{total time}}\)

She goes \(x\) miles out and \(x\) miles back, so her total distance is \(x+x=2x\).

She travels outbound at 10 mph, which we can write as \(t_1=\frac{x}{10}\) hours. She returns at 8 mph, which we can write as \(t_2=\frac{x}{8}\) hours.

\(T_{\text{total}}=\frac{x}{10}+\frac{x}{8}\)\(=x(\frac{1}{10}+\frac{1}{8})=x(\frac{4+5}{40})=\frac{9x}{40}\)

Now you can find the average speed:

\(v_{\text{avg}}=\frac{D_{\text{total}}}{T_{\text{total}}}=\frac{2x}{\frac{9x}{40}}=2x \cdot\frac{40}{9x}\) \(=\frac{80}{9} \approx 8.8889 \text{ mph}\)

First, you need to convert the bed dimensions to feet.

\(1\text{ yd}= 3\text{ ft}\)

\(6\text{ yd}= 6 \times 3\text{ ft}= 18\text{ ft}\)

Then, you need to find the perimeter and account for two rows.

\(P=2(18\text{ ft} + 3\text{ ft})=2\times 21\text{ ft}= 42\text{ ft}\)

\(2\times 42\text{ ft}= 84\text{ ft}\)

Next, determine how many bricks are needed. Since each brick covers 1 foot, you’ll need 84 bricks total. Now you can figure out the total cost.

\(84\text{ bricks}\times \frac{\$2.32}{\text{brick}}=84\times2.32\) \(=\$194.88\)

The equation may be solved for \(x\) by first subtracting \(6x\) from both sides of the equation. Doing so gives \(-3x = -15\), where \(x = 5\).

Substituting 5 for \(x\) into the second expression gives \(5 + 8\), which equals 13.

There are 1,000 milliliters in 1 liter.

The problem may be modeled with the equation \(6.50 = 5.00 + 0.50x\), where \(x\) represents the number of passengers. Solving for \(x\) gives \(x = 3\). Thus, there were 3 passengers, plus 1 driver, for a total of 4 people in the vehicle.

This problem may be represented as \(\frac{1}{9}\times 9\), which equals 1.

Taking out 3 of each color will ensure that he has 1 of each color. Thus, he needs to take out 9 marbles total.

First, we know that 0.20% means 0.20 per 100, so we can write that as follows:

\(0.20%=\frac{0.20}{100}=0.002\)

Now we can turn it into a fraction.

\(0.002=\frac{2}{1,000}=\frac{1}{500}\)

The increase from term to term is twice the increase from the previous two terms. Thus, the increase from 19 to the missing term will be 20, or twice the increase of 10. Thus, the missing term is equal to \(19 + 20\), or 39.

The solution may be modeled by the expression \(0.25(2,490)\). Thus, her budget allowed $622.50 for housing in April.

First, we need to determine the clothing allowance rate. The chart tells us that Jessica devotes 10% of her earnings to clothing each month.

Next, we need to find her total earnings for six months.

\(2,578+2,432+2,668+2,490\) \(+2,622+2,555=15,345\)

Then, we need to figure out her average monthly earnings.

\(\frac{15,345}{6}=2,557.50\)

Finally, we need to calculate 10% for clothing.

\(0.10\times 2,557.50=255.75\)

The amount she saved may be represented by the expression \(0.25(2622) – 0.20(2622)\), which equals 131.10. Thus, she saved $131.10.

First, we need to find each person’s painting rate in fences per hour.

• Kadyn: \(\frac{1}{6}\)
• Ben: \(\frac{1}{8}\)
• Tiana: \(\frac{1}{12}\)

Then, we need to add the rates to get the combined rate.

\(\frac{1}{6}+\frac{1}{8}+\frac{1}{12}=\frac{4+3+2}{24}=\frac{9}{24}\) \(=\frac{3}{8}\text{ fence/hour}\)

Next, we need to invert to find the time.

\(\text{Time}=\frac{1}{\text{rate}}=\frac{1}{\frac{3}{8}}=\frac{8}{3}\text{hours}\) \(=2\frac{2}{3}\text{hours}\)

Finally, we need to convert \(2\frac{2}{3}\) hours to “hours + minutes.”

\(0.6667\text{ hr}\times 60\text{ min/hr}= 40\text{ minutes}\)

So together they take 2 hours and 40 minutes.

The fraction \(\frac{3}{5}\) equals 0.6, which is less than \(\frac{2}{3}\).

The ratio may be written as \(\frac{6}{14}\), which reduces to \(\frac{3}{7}\).

The amount of money she made may be represented by the expression \(90 + 0.12x\), where \(x\) represents the amount of sales. Substituting 3,000 for \(x\) gives \(90 + 0.12(3,000)\), which equals 450. So, she made $450 this week.

First, the perimeter measurement may be converted to feet. Multiplying 25\(\frac{1}{3}\) yards by 3 gives an equivalent measurement of 76 feet.

Thus, the equation may be written \(76 = 2(22) + 2w\), which simplifies to \(76 = 44 + 2w\), where \(w\) = 16.

The problem may be modeled with the expression \(15,000 + 0.15(15,000)\), which equals 17,250. Thus, he sold the boat for $17,250.

We know that 0.15% means 0.15 per 100.

\(0.15%=\frac{0.15}{100}=0.0015\)

Now we need to turn 0.0015 into a fraction.

\(0.0015=\frac{15}{10,000}=\frac{3}{2,000}\)

Moving the decimal point four places to the right gives us 63,340.

Solving the equation for \(x\) gives \(x = -1\). Substitution of -1 for \(x\) in the second equation gives \(-1 + 1 = 0\).

The interior angle measures of a triangle sum to 180°. Thus, the measure of the third angle is equal to the difference of 180° and 120°, which is 60°.

Cups is an appropriate measure of capacity for sugar.