# GED Math : Single-Variable Algebra

## Example Questions

Sixty-four coins, all dimes and nickels, total $5.15. How many of the coins are dimes? Possible Answers: Correct answer: Explanation: Let be the number of dimes. Then there are nickels. An equation can be set up and solved for for the amount of money: , the number of dimes. ### Example Question #1 : Word Problems In Algebra Above is the menu for a coffee shop; there is no sales tax charged on purchases. Greg is throwing a party and wants to buy eight large cappucinos, one for each attendee. He wants to buy all the butter croissants he can without spending more than$80 total. How many croissants will he be able to buy?

Explanation:

Eight large cappucinos will cost Greg

.

This leaves him

to buy croissants, which cost .

Let  be the number of croissants he buys. Then

Greg can buy up to 21 croissants.

### Example Question #11 : Word Problems In Algebra

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?

Explanation:

Let  be 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 #11 : Word Problems In Algebra 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.

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

Explanation:

The number of pounds of coffee beans totals 50, so 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 is dollars. Similarly, the total price of the Ethiopian delight beans is dollars, and the price of the mixture is dollars. 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 #691 : Ged Math 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 has dimes, 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 has nickels. Also, since she has four more quarters than dimes, she has quarters. She has in nickels, in dimes, and in quarters. In total, the number of dollars Leslie has is Leslie has dollars. ### Example Question #11 : Word Problems In Algebra 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 #12 : Word Problems In Algebra 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?

$583.37$580.37

$592.37$573.37

$577.37 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 #15 : Word Problems In Algebra

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

Explanation:

Every word problem has an unknown number. In this problem, the unknown number or value is the price of the shirt.  The variable  will represent the unknown number.

In 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.

In 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 #11 : Word Problems In Algebra

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 make  of them?  (Presume that they make the houses separately and do not interfere with each other's work.)

months

months

Cannot be computed from the data given

months

months

months

Explanation:

This kind of question is really just a basic rate problem.  What it is asking is "How many months  at rate  does it take to make  birdhouses?"  The  rate is just the combination of the two men's rates:

Thus, you can set up the equation:

Thus,

### Example Question #141 : Algebra

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

Explanation:

To solve this equation, first get everything into the same units.  Recall that there are ml for every one liter.  Thus,  liters are equal to  ml.  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 the  ml.  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 you  hours.