GED Math : Word Problems in Algebra

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #143 :代数

The French club wants to make and sell some pizzas for a fundraiser. It will cost $250 to rent the equipment to make the pizzas and $2 worth of ingredients to make each pizza. The pizzas will be sold for $4.50 apiece.

How many pizzas must be made and sold for the French club to make a profit of at least $500?

Possible Answers:

Correct answer:

Explanation:

Letbe the number of pizzas made and sold. Each pizza will require $2 worth of ingredients, so the ingredients in total will cost. Add this to the cost to rent the equipment and the cost will be.

The pizzas will cost $4.50 each, so the money raised will be.

The profit will be the difference between the revenue and the cost:

The French club wants a profit of at least $500, so we set up and solve the inequality:

At least 300 pizzas must be made and sold.

Example Question #144 :代数

Jeff, the barista at Moonbucks Coffee, is having a problem. He needs to make fifty pounds of Premium Blend coffee by mixing together some Kona beans, which cost $24 per pound, with some Ethiopian Delight beans, which cost $10 per pound. The Premium Blend coffee will cost $14.20 per pound. Also, the coffee will sell for the same price mixed as it would separately.

Letbe the number of pounds of Kona beans andbe the number of pounds of Ethiopian Delight beans. Which of the following systems of equations could you set up to solve this problem?

Possible Answers:

Correct answer:

Explanation:

50磅的咖啡豆总数的数量,one of the equations would be

.

The total price of the Kona beans is the unit price, $24 per pound, multiplied by the quantity,pounds. This isdollars. Similarly, the total price of the Ethiopian delight beans isdollars, and the price of the mixture isdollars. Add the prices of the Kona and Ethiopian Delight beans to get the price of the mixture:

These are the equations of the system.

Example Question #145 :代数

Leslie has some nickels, some dimes, and some quarters. She has twice as many dimes as she has nickels, and she has four more quarters than she has dimes. If she hasdimes, how much does she have, in terms of, in nickels, dimes, and quarters?

Possible Answers:

dollars

dollars

dollars

dollars

Correct answer:

dollars

Explanation:

Since Leslie has twice as many dimes as nickels, the number of nickels she has is half the number of dimes, or half of. This means she hasnickels. Also, since she has four more quarters than dimes, she hasquarters.

She has

in nickels,

in dimes, and

in quarters.

我n total, the number of dollars Leslie has is

Leslie hasdollars.

Example Question #146 :代数

John had 48 candies. He ate 2, and said he gave almost 25% of the remaining to charity. What is the most reasonable number of candies he had left?

Possible Answers:

Correct answer:

Explanation:

After John has ate 2 candies out of his total of 48 candies, he has 46 candies left.

25% of 46 is equivalent to:

However, candies are counted in units, which means if John could have only given 11 candies to charity if he said he has given almost 25% away. The trick answer is 34 because 11.5 candies cannot be rounded to 12 candies.

Hence:

Example Question #147 :代数

Suppose a customer paid $500 for a new phone. The store had applied a 20% discount, and the tax after the discount was 8.25%. What was the approximate price of the phone before the applied discount and tax rate?

Possible Answers:

$577.37

$580.37

$592.37

$583.37

$573.37

Correct answer:

$577.37

Explanation:

Let x be the cost of the phone before applying the 20% discount. After applying the discount, the value will be equal to some amount y before applying tax.

After amount y has been taxed the 8.25%, the new value will be the price of the phone, which is $500. The equation representing this relationship is:

We have a system of equations. Substitute y in terms of x into the 2nd equation. Solving the value of x will give the original value of the phone.

Therefore, the price of the phone is approximately $577.37.

Example Question #148 :代数

米ary spent $48 for shoes. This was $14 less than twice what she spent for a shirt. How much was the shirt?

Possible Answers:

Correct answer:

Explanation:

Every word problem has anunknownnumber. In this problem, the unknown number or value is the price of the shirt. The variablewillrepresent the unknown number.

我n this problem,will represent how much Mary spent for the shirt. The problem states that $48 was $14 less than 2 times what she spent on for the shirt. An equation will be written in order to solve this problem.

Then solve for.

The first step is to remove the subtraction of $14 by using the inverse operation, which would be addition. Remember, because it is an equation, whatever operation you choose to perform on one side of the equation must also be done to the other side of the equation. Therefore, you will add $14 to both sides of this equation.

我n order to solve for, you will need to divide both sides by the coefficient, (the number next to the variable), which is 2.

Example Question #149 :代数

Pat makes fifteen birdhouses every month, while John makes twenty. If the two men work together to make birdhouses, how long will it take them to makeof them? (Presume that they make the houses separately and do not interfere with each other's work.)

Possible Answers:

months

months

Cannot be computed from the data given

months

months

Correct answer:

months

Explanation:

This kind of question is really just a basic rate problem. What it is asking is "How many monthsat ratedoes it take to make鸟屋?”率是t的组合he two men's rates:

Thus, you can set up the equation:

Thus,

Example Question #150 :代数

A tank leaks at a rate ofml per second. How many hours will it take for the tank to drain, given that it isliters? Round to the nearest hour.

Possible Answers:

Correct answer:

Explanation:

To solve this equation, first get everything into the same units. Recall that there areml for every one liter. Thus,liters are equal toml. Now, what you basically have is a rate equation. Recall that the total work is represented as follows:

For your data, the total "work" is theml. Start by calculating the time as a decimal:

This gives you:

However, remember that this is in seconds. You need to convert back to hours. You do this by dividing by, giving you. Rounding up, this gives youhours.

Example Question #11 :Word Problems In Algebra

A writer makedollars of profit per book sold. The printing run of a lot ofbooks costdollars. How many books must the author sell before the book becomes profitable?

Possible Answers:

Correct answer:

Explanation:

This question could be set up like an equation as follows:

The variableindicates the number of books that would have to be sold. This comes out to:

Now, don't be tricked! You can't sell partial books. Thus, you will need to sellbooks in order to turn a profit. If you only sell, you will not have sold enough to make a profit.

Example Question #12 :Word Problems In Algebra

An author writes a book that sells fordollars. He haspublished at a cost ofdollars per book. How many books must he sell before his profit is at leastdollars per book?

Possible Answers:

books

books

books

books

books

Correct answer:

books

Explanation:

This question is a bit hard. You need to think it out step by step. First, you could write an equation like this:

This represents the idea of trying to calculate when the profit per book will be three dollars. Now, we know that profit is equal to:

Thus, you can rewrite your equation:

Now, the original cost is calculated by multiplyingby. This is the same as. The sales amount is just, whereindicates the total number of books sold. This will also be the total forin your equation. Thus, you can write out the following equation:

Now, just solve for:

However, you will need to sell one more book than. (That would be just a little too insufficient.) Thus, the answer is.

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