Pre-Algebra

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Math › Pre-Algebra

Questions 1 - 10

Evaluate:

Explanation

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Solve by dividing on both sides of the equation. Move the decimal two places to the right.

$\frac{0.09x}{0.09} = \frac{27}{0.09} =\frac{2700}{9}$

Now factor the numerator to find values that can cancel out.

$\frac{2700}{9}=\frac{9\cdot 300}{9}$

The nine in the numerator and denominator reduce to one and we are left with our final answer,

Solve for .

Explanation

Subtract from both sides.

Rojo Salsa is on sale at a price of $\$ 9$ for jars of ounces each. Verde Salsa is on sale at a price of $\$8$ for jars of ounces each. Which of the following statements is true?

An ounce of Rojo Salsa is the same price as an ounce of Verde Salsa.

An ounce of Verde Salsa costs more than an ounce of Rojo Salsa.

A jar of Verde Salsa costs more than a jar of Rojo Salsa.

Verde salsa sells at $\$ 0.40$ per ounce.

An ounce of Rojo Salsa costs more than an ounce of Verde Salsa.

Explanation

The statement "A jar of Verde Salsa costs more than a jar of Rojo Salsa" can be tested by comparing the price per jar of each salsa.

$\frac{\$9}{3 \ jars \ Rojo} = \$3 \ per \ jar$ versus $\frac{\$8}{4 \ jars \ Verde} = \$2 \ per \ jar$

The statement is false since the price of Rojo per jar is greater.

The remaining statements above can all be proven true or false by finding the price per ounce of each salsa.

Rojo Salsa is on sale at a price of $\$ 9$ for jars of ounces each. The following operations can be used to determine the cost of Rojo Salsa per ounce:

$3 \ jars \times 12 \ ounces \ per \ jar =36 \ ounces \ sold \ per \ \$9$

$\rightarrow \$9 = 36 \ ounces \rightarrow \$ \frac{9}{36} = 1 \ ounce \rightarrow \$ \frac{1}{4} \ per \ ounce$

$\rightarrow \$0.25 \ per \ ounce$ for Rojo Salsa.

Verde Salsa is on sale at a price of $\$8$ for jars of ounces each. The following operations can be used to determine the cost of Verde Salsa per ounce.

$4 \ jars \times 8 \ ounces \ per \ jar =32 \ ounces \ sold \ per \ \$8$

$\rightarrow \$8 = 32 \ ounces \rightarrow \$ \frac{8}{32} = 1 \ ounce \rightarrow \$ \frac{1}{4} \ per \ ounce$

$\rightarrow \$0.25 \ per \ ounce$ for Verde Salsa.

The only true statement is "An ounce of Rojo Salsa is the same price as an ounce of Verde Salsa."

What is ?

Explanation

Recall that subtracting integers is equivalent to adding the inverse. The inverse of a negative number is the positive number with the same magnitude.

Thus, our problem is equivalent to .

Rojo Salsa is on sale at a price of $\$ 9$ for jars of ounces each. Verde Salsa is on sale at a price of $\$8$ for jars of ounces each. Which of the following statements is true?

An ounce of Rojo Salsa is the same price as an ounce of Verde Salsa.

An ounce of Verde Salsa costs more than an ounce of Rojo Salsa.

A jar of Verde Salsa costs more than a jar of Rojo Salsa.

Verde salsa sells at $\$ 0.40$ per ounce.

An ounce of Rojo Salsa costs more than an ounce of Verde Salsa.

Explanation

The statement "A jar of Verde Salsa costs more than a jar of Rojo Salsa" can be tested by comparing the price per jar of each salsa.

$\frac{\$9}{3 \ jars \ Rojo} = \$3 \ per \ jar$ versus $\frac{\$8}{4 \ jars \ Verde} = \$2 \ per \ jar$

The statement is false since the price of Rojo per jar is greater.

The remaining statements above can all be proven true or false by finding the price per ounce of each salsa.

Rojo Salsa is on sale at a price of $\$ 9$ for jars of ounces each. The following operations can be used to determine the cost of Rojo Salsa per ounce:

$3 \ jars \times 12 \ ounces \ per \ jar =36 \ ounces \ sold \ per \ \$9$

$\rightarrow \$9 = 36 \ ounces \rightarrow \$ \frac{9}{36} = 1 \ ounce \rightarrow \$ \frac{1}{4} \ per \ ounce$

$\rightarrow \$0.25 \ per \ ounce$ for Rojo Salsa.

Verde Salsa is on sale at a price of $\$8$ for jars of ounces each. The following operations can be used to determine the cost of Verde Salsa per ounce.

$4 \ jars \times 8 \ ounces \ per \ jar =32 \ ounces \ sold \ per \ \$8$

$\rightarrow \$8 = 32 \ ounces \rightarrow \$ \frac{8}{32} = 1 \ ounce \rightarrow \$ \frac{1}{4} \ per \ ounce$

$\rightarrow \$0.25 \ per \ ounce$ for Verde Salsa.

The only true statement is "An ounce of Rojo Salsa is the same price as an ounce of Verde Salsa."

Solve for .

Explanation

To solve for , the first thing we need to do is isolate the variable. That means we want ONLY on the left side of the equation.

Divide both sides by .

$\frac{2x}{2}=\frac{32}{2}$

$x=\frac{32}{2}$

A farmer has units of fence. If he uses this to build a square fence, what will be the length of each side?

Explanation

If this is a square fence, then each of the four sides will be equal.

The fence in question will become the perimeter of that square.

Since when working with a square, for this problem .

$\frac{100}{4}=s$

A farmer wants to build a rectangular fence to enclose a $144\ \textup{ft}^2$ yard. If the yard is square, how many feet of fence will he need?

$48\ \textup{ft}$

$144\ \textup{ft}$

$576\ \textup{ft}$

$36\ \textup{ft}$

$12\ \textup{ft}$

Explanation

The area of a square is . Since our area is ,

Take the square root of both sides.

$\sqrt{144ft^2}=\sqrt{s^2}$

The perimeter of a square is the sum of all four sides. Since all sides are equal, we can say that, for a square, the formula for a perimter would be .

Plug in what we just found:

Solve for if $x+\frac{1}{4}=\frac{3}{8}$

$x=\frac{1}{8}$

$x=\frac{3}{4}$

$x=\frac{3}{8}$

$x=\frac{1}{2}$

Explanation

To solve for we must get all of the numbers on the other side of the equation of .

To do this in a problem where a number is being added to , we must subtract the number from both sides of the equation.

In this case the number is $\frac{1}{4}$ so we subtract $\frac{1}{4}$ from each side of the equation to make it look like this $x+\frac{1}{4}-\frac{1}{4}=\frac{3}{8}-\frac{1}{4}$

To subtract fractions we must first ensure that we have the same denominator which is the bottom part of the fraction.

To do this we must find the least common multiple of the denominators.

The least common multiple is the smallest number that multiples of both of the denominators multiply to.

In this case the LCM is

We then multiply the numerator and denominator of $\frac{1}{4}$ by to get the same denominator because anything divided by itself is one so the fractions maintain their same value as the numbers change into the format we need to determine the answer.

To multiply a fraction you multiply the top number of the first fraction by the top number of the second fraction and the bottom number of the first fraction by the bottom number of the second fraction so it would look like this $\frac{1}{4}*\frac{2}{2}=\frac{2}{8}$

After doing this we then subtract the first numerator (top part of the fraction) from the second numerator and place the result over the new denominator $x=\frac{3}{8}-\frac{2}{8}$