Rob S.

Graduate student with experience tutoring elementary and high school math and science

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Basic Math

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Question:

A shirt is on sale for 60% off. The original price of the shirt is $50. What is the new price of the shirt?

Rob S.

Answer:

To find the new price of the shirt, we start by multiplying the original price ($50) by the sale percentage (60%). This gives us the discount on the shirt. ($50)(60%)=($50)(.6)=$30. This tells us that the shirt has been discounted by $30. To find the new price, we have to subtract the discount from the original price. $50-$30 = $20 Therefore, the new cost of the shirt is $20

ASVAB

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Question:

A truck rental company charges $500 to rent a truck It charges an additional $0.50 per mile driven for the first 100 miles, and $0.20 for every mile traveled after that. If you need to travel 500 miles with this truck, how much money will you pay?

Rob S.

Answer:

To start with, we should create an equation that represents the total cost for a certain number of miles traveled. The best way to do that is to break the information we have down into easily manageable pieces. The first piece of information we have is that there is a flat rate of $500 to rent the truck. There will always be a minimum charge of $500, even if we only drive one mile. Right off the bat, our equation for Rental Cost (RC) is: RC = $500 The second piece of information given to us is that there is another charge of $0.50 per mile driven for the first 100 miles. Since we are just trying to write an equation, we don't need to know how many miles we are driving. Instead, we can just call miles driven "x", and we know that x has a maximum value of 100 (because anything after that has a different cost" We know, therefore, that this first Mileage cost is equal to ($0.50)x, where x is the number of miles We know that we will always have to pay $500 for the truck, so we have to add the mileage cost to the cost of the truck to get the actual cost. Our new cost with the truck included is $500+($0.50)x. Finally, the third piece of information given is that for every mile after 100 miles, there is a $0.20 cost. Let us call the number of miles we drive after driving 100 miles "y". That’s a bit confusing, so to clarify: If we drive 90 miles, we never hit 100 miles, so y=0 (since we don't drive more than 100 miles). If we drive 100 miles, we still aren't driving more than 100 miles, so y still equals 0. If we drive 101 miles, however, we drive 1 mile after reaching 100 miles, so y=1. If we drive 150 miles, then we travel 50 more miles after reaching 100 miles, so y =50. Now that we have y clarified, we know that the cost after 100 miles is $0.20y. This is in addition to the cost of the truck and the first 100 miles, so we have to add all these numbers together to get the total cost. Total Cost (TC) = Cost of rental + mileage cost for first 100 miles + mileage cost for every mile after Using the numbers we figured out, we have: TC = $500+$0.50x+$0.20y Now that we have an equation written, we can solve for the cost if we drive 500 miles. The first thing to figure out is the variables. We are traveling 500 miles, and we know that x is 100 miles (because the charge only applies for the first 100 miles). This leaves us with 400 miles left, so y=400 (we travel an additional 400 miles after first traveling 100 miles). Plugging these numbers into our equation gives us: TC = $500+($0.50)(100)+($0.20)(400) Solving this out gives us: TC = $500+$50+$80 TC = $630 Our final cost is $630.

Algebra

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Question:

Solve the system of equations 3x+2y=12 9x-3y=9

Rob S.

Answer:

To start with, let us label our equations. We will call 3x+2y=12 equation one and 9x-3y=9 equation two. 1) 3x+2y=12 2) 9x-3y=9 To solve the system of equations, we need to pick a variable to solve for first. Then we need to cancel the other variable so we can solve for the variable we want. Let us say that we want to solve for y first. If we look at equation 1, we can see that if we multiply the equation by -3, we will have -9x, which will cancel the 9x in equation 2. 1) (-3)(3x+2y)=(12)(-3) Solving this out gives us: 1) -9x-6y=-36 Now we will add the two equations together: 1) -9x-6y=-36 2) 9x-3y= 9 0 -9y=-27 -9x+9x gives us 0, so the x's cancel. -6y+(-3y) gives us -9y. On the other side of the equal sign, -36+9 gives us -27 Our new equation is: -9y=-27 To solve for y, we need to get rid of the -9. To do that, we have to divide both sides by -9 (-9y)/(-9)=(-27)/(-9) Solving this gives us: y=3 Now to solve for x, we need to substitute y=3 back into one of our equations. Let us use equation 1: 3x+2(3)=12 3x+6=12 We need to move the 6 to the other side of the equation, so we have to add -6 to both sides 3x+6-6=12-6 3x=6 Now to solve for x, we divide both sides by 3. (3x)/(3)=6/3 x=2 We know x and y now, so our answer is x=2 and y=3. In coordinate form, this is (2,3)

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