Word Problems and Algebraic Equations - Math

To solve this word problem, set up an algebraic equation, putting in for the unknown value of the second shirt. The equation is because we know the cost of the two shirts will total .

To solve for , subtract from each side. This results in .

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."

To find the speed (or rate) that Josef will need to travel, we can use the equation ().

This equation cannot be used for Josef yet, since only the distance traveled is known and not the time in which he will need to make the trip.

To find the time it takes Barbara to make the trip, use the same equation to solve for , where the distance is the length of Barbara's trip. Note that we express miles per hour as a fraction that represents the ratio of miles to hour.

Multiply both sides of the equation by the reciprocal of the rate. Note that the unit of "miles" cancels out, leaving only the unit "hours" (time). The result will be expressed as a fraction of a single hour.

The amount of time it takes Barbara to get to the beach must be the same amount of time it takes Joseph to get to the beach.

Therefore, we can use this new value of and the equation to find the rate Josef will need to travel for his mile trip.

Multiply both sides by the reciprocal of time (a fraction) to isolate the rate.

To find how much additional money Sarah would make by applying the discount, find the difference between her earnings in a normal month and a month where the discount is applied. In a normal month, multiply the normal price by the normal quantity sold to find the normal earnings:

To find earnings at the discounted price, first calculate how much each necklace will cost with the % discount. To do this, subtract the amount discounted (calculated by percent as a fraction of multiplied by the original price) from the original price.

If necklaces are sold at the new discounted price of each, multiply these together to find the total earnings with the discount.

Finally, subtract the earnings without the discount from the earnings with the discount to find the additional money made by applying the discount.

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 .

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 .

First we need to find the area of the smaller rectangle.

Now to find out how many can fit, we divide the total area by the smaller area.

However, the problem is asking how many WHOLE rectangles can fit. Therefore only can fit.

First, use the information to find the total number of socks Eric has by setting up a proportion:

, where is the number of total socks.

Once you cross multiply and divide, you will find that .

To find the number of white socks Eric has, subtract the number of black socks from the total number of socks:

pure water and pure acid

In general, mixture problems have the form:

, where volume and percent

The equation to solve becomes:

Then the solution is .

The cost of mailing each invitation is .

To invite everyone, it will cost .

Then the change is .

Look for the verbal cues in the question. IS translates to "equals" and OF translates to multiplication.

Thus the equation to solve becomes:

Look for the verbal cues in the question. IS represents "equals" and OF represents multiplication.

Then the equation to solve becomes:

so or

In general, a commission problem has the form:

So the commission is:

Money problems generally consist of two parts: total number of coins and total value of money.

Let number of nickles, number of quarters, and number of dimes.

So the equation to solve becomes:

or

so

Thus, , so there are three nickles, eight quarters and seven dimes for a total of coins.

Cut the recipe by four: cookies; however, the question asks for how many DOZENS of cookies are made, so the correct answer is dozen cookies.

Use proportions to solve this problem.

Let quarts of yellow paint.

By cross-multiplying we get .

Since , we actually need .

Use the factor-label method to solve this problem:

For a rectangle:

and

Let width and length.

Thus , so the width is and the length is .

Then the area becomes .

Use the factor-label nethod to solve this problem:

or approximately .

Use proportions to solve this problem:

Let acres worked by Frank and acres worked by George.

Cross-multiply to get or so .

So Frank works and George works .