GED Math Practice

There are "s" steps from the pedestal to the head of the Statue of Liberty. The number of steps in the Washington Monument is 27 less than 6 times the number of steps in the Statue of Liberty. Which expression represents the number of steps in the Washington Monument in terms of s?

To answer this question we have to break down what is being said, we see that "s" is the amount of steps to the top of the statue of liberty(SoL). Next we see that the Washington monument steps are 27 LESS steps than 6 TIMES the number of steps of the SoL. Using the words behind the numbers we can deduce that we will have subtraction and multiplication. We also see that it says 6 TIMES the SoL steps, given that SoL is "s" we can get 6s.Then we see that the washington monument is 27 steps LESS than 6s, which is subtraction. To put it all together 6 Times s with 27 less steps Answer: 6s - 27

A painter rented a wallpaper steamer at 9 a.m. and returned it at 4 p.m. He paid a total of $28.84. What was the rental cost per hour?

9 am - 4 pm = 7 hours $28.84(total paid) / 7(time) = $4.12 Answer: $4.12

Emma needs to order liquid fertilizer for her landscaping company. She plans to keep the fertilizer in a large cylindrical storage tank, but isn't sure how much it will hold. The tank is 10 feet tall and the circular base has a radius of 5 feet. What is the volume of her storage tank?

This question has asked us to find the volume of a cylinder, we must know the formula for the volume of a cylinder. which is π r^2 h r = radius h = height π = pi/3.14 Our given values from the question are r = 5 h = 10 Now all you must do is simply plug in your numbers with their corresponding variables. π r^2 h π (5)^2 (10) using a calculator we get the volume to be 785.4^3 Answer: 785.4^3

Dominic earns $285 per week plus an 8% commission rate on all his sales. If Dominic sells $4,213 worth of merchandise in one week, how much will his total earnings for the week be?

This question is asking for Dominic's gross income for the week, we are told his weekly flat income rate of $285 and his commission rate of 8% on all sales. This week Dominic sold $4,213 worth of merchandise, given his 8% commission on all sales how much will Dominic pocket for the week? *Percents are always put into decimal form in mathematical equations ie. 10% = 0.1, 37% = 0.37, 96% = 0.96, 100% = 1.0 etc* Since Dominic has sold $4,213 worth of merchandise, so we can simply multiply his percentage cut from the total. $4,213(all weekly sales) x 0.08(8% commission on all sales) = 4,213 x 0.08 = $337.04 That is not the end, we are also given his weekly flat rate income of $285, simply add it to the commission. $337.04 + $285 = $622.04 Answer: $622.04

A phone company charges $2 for the first five minutes of a phone call and 30 cents per minute thereafter. If Bill makes a phone call that lasts 25 minutes, what will be the total cost of the phone call?

This question is pretty simple to break it down $2 = first 5 min $0.30 = min after the first 5 We are given that bill makes a 25 minute phone call, using the earlier point we can take off 5 min and add $2. leaving us with 20 minutes. Explained by the equation, $0.30(minute/rate fee after first 5 min) x 20(minutes that bill was on the phone after the first 5) $0.30 x 20 = 6 Using our equation the 20 min after the first 5 costed bill an extra $6, add the first 5 min flat rate fee of $2 and you get bill's total cost for his 25 min phone call. $6 + $2 = $8 *Another way to show this would be $2(flat rate for first 5 min) + 0.30x(x is min after first 5). 2 + 0.30x or for us 2 + 0.30(20)* Answer: $8

If y = 3ab + 2b^3, what is y when a = 1 and b = 2?

This question really gives you all the tools necessary to solve it simply, all you must do is plug the numbers with the corresponding variable. a = 1 b = 2 3ab + 2b^3 = 3(1)(2) + 2(2)^3 3 x 1 = 3 x 2 = 6 2 cubed(^3) is 2 x 2 x 2 2 x 2 = 4 x 2 = 8 8 x 2( last 2 is from the one outside the parentheses) = 16 6 + 16 = y y = 22

Annie is planning a business meeting for her company. She has a budget of $1,325 for renting a meeting room at a local hotel and providing lunch. She expects 26 people to attend the meeting. The cost of renting the meeting room is $270. Which inequality shows how to find the amount, x, Annie can spend on lunch for each person? A. 26x + 270 ≥ 1,325 B. 26x + 270 ≤ 1,325 C. 270x + 26 ≥ 1,325 D. 270x + 26 ≤ 1,325

First you must denote that the problem says her spending LIMIT is $1,325, meaning she must either spend LESS OR EQUAL to $1,325. Given this we can cross out A and C since they have the expression worth MORE than $1,325, leaving us with B and D. The room rental is a FLAT rate and does not have any variance, however lunches are variable by the amount of attendees. given this information the variable will be placed with the 26 people and their lunches. Answer: B

An office uses paper drinking cups in the shape of a cone, with dimensions as shown. Height(H) = 4 In Width/Diameter = 2.75 In To the nearest tenth of a cubic inch, what is the volume of each drinking cup?

So we are asked to find the volume of a cone, to do this we must know the equation for the volume of a cone. Volume of a cone = π (r)^2 H/3 π = Pi/3.14 r^2 = Radius(half of diameter) H = Height Now lets get our radius so we can plug in our numbers r = diameter/2 2.75/2 = 1.375 Now to plug our numbers into the volume equation r = 1.375 H = 4 Volume of a cone = π(1.375)^2 4/3 Using a calculator we get the Volume of this cone to be 7.92 *Volume is always CUBED, which means the volume answer will be (n)^3, Area and Perimeter will always be SQUARED or (n)^2* Answer: 7.92^3

Which of the following expressions is equivalent to 3x(2 + 5y)?

This is what's called the distributive property, you see that the equation reads as 3x times the sum of (2 + 5y). instead of going through the loophole you can just multiply all the items in the parentheses by 3x. To show 3x(2 + 5y) = (3x x 2) + (3x x 5y) Since the question is asking for an EQUAL EQUATION and not the values of x and y we can simply solve the equation in the parentheses. (3x x 2) = 6x (3x x 5y) = !5xy *When multiplying numbers with variables (x, y, etc) the number in front of the variable is called the coefficient ie in 3x the "3" is the coefficient. when multiplying these variables the numbers will only affect the coefficient and not the variable ie 3y x 3 = 9y and NOT 9y^3. Different variables multiplied will share the coefficient, ie 4z x 15y = 60xy* Answer: 6x + 15xy

What is the value of 36x - 8y^2 given that x = 3 and y = -6?

Plug in x and y 36(3) - 8(-6)^2 *Any negative number SQUARED(^2) will become positive since a negative times a negative is positive* -6^2 = 36 36(3) - 8(36) = 108 -288 108 - 288 = -180 Answer: -180