# Tutor profile: Emily M.

## Questions

### Subject: Geometry

Kyle just built a trapezoid-shaped deck. The bases of the trapezoid measure 40 feet and 25 feet and its height is 20 feet. Each can of stain costs $10.25 and covers 70 square feet. How much will it cost him to buy enough stain to cover his deck?

The question asks us to calculate cost. To figure out the cost, we need to know how many cans he must buy. We know each can costs $10.25 and covers 70 square feet. Square feet is a unit for area, so we need to find the area of the deck in order to figure out how many cans he needs to buy. Area of a trapezoid is (1/2)*(base + base)*height. A = (1/2)*(40 + 25)*20 Use the order of operations to simplify. A = (1/2)*(65)*20 A = 32.5*20 A = 650 square feet We know each can of stain covers 70 square feet. If we divide the total area by 70, we will know how many cans Kyle must buy. 650/70 = 9.2857... Since this is a real-life situation, we know Kyle must buy whole cans. 9 cans wouldn't be quite enough, so he must buy 10 cans. Now we can calculate cost. Each can costs $10.25. If we multiply that by the number of cans Kyle needs to buy, we will know the total cost. $10.25 * 10 = $102.50 It will cost Kyle $102.50.

### Subject: Pre-Algebra

A ladder is leaning against a wall. The ladder is 12 feet long. The foot of the ladder is 5 feet away from the wall. How high up the wall will the ladder reach? Round to the nearest tenth.

Let's draw a picture and label it with the numbers from the problem. I know the wall is going to go straight up and down, but we don't know how high it is. Let's label that line "x." The ladder is leaning against it at an angle and it's 12 feet long. Let's label the slanted line "12 ft." The "foot" of the ladder means the "bottom" of the ladder. The space between the bottom of the ladder and the wall is 5 feet. Let's draw a line between the bottom of the wall and the bottom of the ladder. It should be straight across because the ground is flat. Your picture should look like this: |\ | \ 12 ft x | \ |___\ 5ft Because this triangle has a right angle and we are working with all three sides, we can use the Pythagorean Theorem (a² + b² = c²). "c" always represents the hypotenuse, which is the side that is opposite of the right angle (the slanted side). "a" and "b" are the legs, which are the sides that make the right angle (the straight sides). x² + 5² = 12² 5² = 5 * 5 = 25 and 12² = 12 * 12 = 144 So, x² + 25 = 144 We need to solve for x. Start by getting the "x²" by itself. 25 is being added to it. The inverse of adding is subtracting. Let's subtract 25 from both sides of the equation (to keep both sides equal). x² + 25 - 25 = 144 - 25 x² = 119 We need to get just "x" by itself. The inverse of squared is square root. Let's take the square root of both sides of the equation. √x² =√ 119 √ 119 = 14.1067... The question said to round to the nearest tenth, which is one number after the decimal. We need to decide if we should leave it as 14.1 or round up to 14.2. We look at the next number (0). If it is 5 or higher, we round up. Since it's not, we leave it as 14.1. x = 14.1 feet

### Subject: Algebra

A bracelet costs $4.00. If the sales tax is 6%, what is the total price?

First, we need to figure out how much money the sales tax is (6% of $4.00). There are two ways to figure this out. We could use proportions to figure this out. Let's use "x" to represent the amount of sales tax. Percent means "out of 100", so the proportion would be 6/100 = x/4.00. There are two ways to solve for x in this proportion. 1. First, we could simplify the left side by dividing. 6/100 = .06. So our new proportion is .06 = x/4.00 "x" is being divided by 4. The inverse of division is multiplication. We can multiply both sides (to keep both sides equal) of the equation by 4 to get the "x" by itself. 4 * .06 = 0.24. So 0.24 = x. The sales tax is $0.24. 2. A different way you may have been taught to solve proportions is by "cross multiplication." Start with the same proportion 6/100 = x/4.00. When you cross multiply you take the numerator (top) of one side times the denominator (bottom) of the other side of the equation. 6 * 4 = x * 100 Simplify the left side. 6 * 4 = 24. 24 = x * 100 "x" is being multiplied by 100. Division is the inverse of multiplication. We can divide both sides (to keep both sides equal) of the equation by 100 to get the "x" by itself. 24/100 = 0.24. So 0.24 = x. The sales tax is $0.24. Sales tax makes the total price more than $4.00, which means we have to add the sales tax to the price. 4.00 + 0.24 = 4.24 The total price is $4.24.

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