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Jason L.

Student of University of Pennsylvania

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Pre-Algebra

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Question:

Solve this proportion: 8/35 = 50/x

Jason L.

Answer:

In order to solve this proportion, we want to solve for x. There are two ways to do this and both ways will give you the same answer. Method 1: For proportions, the ratio of the numerators and denominators must be the same. Therefore, we can solve for the ratio of the numerators and then apply that ratio to the denominators to solve for x. First, we do 50/8 = 6.25. This means the ratio of the numerators is 6.25:1. Since we have to multiply 8 by 6.25 to get 50, we will multiply 35 by 6.25 to get x. 35*6.25 = x x = 218.75 Method 2: We can isolate x using multiplication and division. First, we should multiply both sides by x to get x*(8/35) = 50. Next, we should divide each side by 8/35. (We could also multiply each side by 35/8.) This will give us x = 50/(8/35) = 218.75 Notice how both methods give you the same answer so you can choose whichever method you feel most comfortable with.

Basic Chemistry

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Question:

What is the mass of 9.03*10^23 molecules of NaCl?

Jason L.

Answer:

First, let's figure out how many atoms are in one mole. From Avogadro's number, we know that there are 6.02*10^23 atoms in a mole. The ratio of Na+ to Cl- atoms is 1:1 because the subscripts for each element is 1. It is implied that when there is not subscript on an element, the subscript is 1. Since we have 9.02*10^23 molecules of NaCl we divide 9.03*10^23 by 6.02*10^23 in order to figure out how many moles of NaCl we have. 9.03*10^23 / 6.02*10^23 = 1.5 So, we have 1.5 moles of NaCl. Next, we have to find the molar mass of NaCl. In order to do this, we look at the periodic table and add the molar masses of Na+ and Cl -. The molar mass of Na+ is 22.99g and the molar mass of Cl- is 35.45g. So the molar mass of NaCl is: 22.99g + 35.45g = 58.44g In order to find out the mass of 1.5 moles (9.03*10^23 molecules) of NaCl, we have to multiply the molar mass of NaCl by the number of moles we have. 58.44*1.5 = 87.66g

Algebra

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Question:

Solve for x: 6(x-2)+7 = 3(x-3)-2

Jason L.

Answer:

6(x-2)+7 = 3(x-3)-2 For this problem, we will follow PEMDAS. First, we need to deal with the parentheses so we should distribute on both sides to get: 6x-12+7 = 3x-9-2 Next, we need to combine like terms. Combine all the terms without an x to get: 6x-5 = 3x-11 Then isolate the x terms to get: 3x = -6 Finally, isolate x to get: x = -2 Congratulations! You have solved the problem.

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