Algebraic Equations
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Rojo Salsa is on sale at a price of for
jars of
ounces each. Verde Salsa is on sale at a price of
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 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.
versus
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 for
jars of
ounces each. The following operations can be used to determine the cost of Rojo Salsa per ounce:
for Rojo Salsa.
Verde Salsa is on sale at a price of for
jars of
ounces each. The following operations can be used to determine the cost of Verde Salsa 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 .
Solve for .
Explanation
Subtract from both sides.
A shirt costs $12 after a 15% discount. What was the original price of the shirt?
Explanation
Convert 15% to a decimal.
Let the original price equal . The discount will be 15% of
. Subtracting the discount from the original price will equal the amount paid, $12.
Using this equation, we can solve for .
Solve for .
Explanation
Subtract from both sides.
Solve for if
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 so we subtract
from each side of the equation to make it look like this
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 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
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
The final answer is
Solve for if
Explanation
To solve for we must get all of the numbers on the other side of the equation as
.
To do this in a problem where is being divided by a number, we must multiply both sides of the equation by the number.
In this case the number is so we multiply each side of the equation by
to make it look like this
The 's on the left side cancel so we only have
.
Then we perform the necessary multiplication to get the answer of .
Solve for .
Explanation
To solve equations, you must perform the same operations on both sides.
Subtract 5 from both sides.
Solve for if
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 so we subtract
from each side of the equation to make it look like this
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 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
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
The final answer is
A shirt costs $12 after a 15% discount. What was the original price of the shirt?
Explanation
Convert 15% to a decimal.
Let the original price equal . The discount will be 15% of
. Subtracting the discount from the original price will equal the amount paid, $12.
Using this equation, we can solve for .