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David, Post-Doctoral Degree
Category: Math Homework
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Experience:  Theoretical Physics
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Hi, I have eight math questions for my 8th grade daughter.

Hi,
I have eight math questions for my 8th grade daughter. Her school is teaching 9th grade algebra. I am awful at math and in order to help her I would appreciate it if you show the work for each question so that I can go over it with her and explain each one. I will send one at a time. The numbers are 32. to 40. and I will number them as such. Here goes the first one:
32. A baseball tema played 162 games and won 90.
a. What is the ratio of the number of games won to the number of games played?
b. For every nine games played, how many games were won?

David :

hello, I'll be glad to assist.
a. 90/162 = 5/9
b. as you see from a) the answer is 5 (five out of nine)

David :

hope this helps

Customer:

How did you turn the decimal into a fracion for a.?

David :

what decimal?

David :

ration means divide

David :

so you need to divide 90 by 162

Customer:

right and when you divided you got a decimal, no?

David :

no I did not get decimal I simplifyed the frction as follows:

David :

90/162= 9*10 / 9*18 = 10 / 18 = 5*2/ 9*2 = 5/9

David :

does it make sense now?

Customer:

Sorry, I told you math is not my strong point. okay, thanks, XXXXX XXXXX one is

Customer:

33. A student did six of ten problems correctly.

Customer:

a. what is the ratio of the number right to the nuimber wrong?

Customer:

b. For every two answers that were wrong, how many answers were right?

David :

a. 6 our of 10 is correct means that 4 are wrong, so the answer is 6/4 = 3/2

David :

b. as you see from the previous part it the answer is 3

Customer:

Okay, just a quick qustion re #32 what does the * mean?

David :

times. for example 90=9*10 read like ninety is equal to nine times ten

Customer:

Ok, thanks.

Customer:

34. A cake recipe calls for 1 1/4 cups of milk to 1 3/4 cups of flour. Write, in simplest form, the ratio of the number of cups of milk to the number of cups of flour in this recipe.

David :

note that 1 1/4 is 5/4 ans 1 3/4 is 7/4 so the ration is (5/4) / (7/4) = 5/7

Customer:

35. The perimeter of a rectangular garden is 30 feet, and the width is 5 feet. Find the ratio of the length of the rectangle to its width in simplest form.

David :

recall that perimeter is 2L+2W, hence we have that 2L=30-10=20, so the length is 10 and hence the ratio is 10/5 = 2

Customer:

36. In a freshman class, there are b boys and g girls. Express the ratio of the number of boys to the total number of pupils.

David :

total people is b+g hence the ration is b/(b+g)

Customer:

37. The length of a rectangular classroom is represented by 3x and its width by 2x. Find the ratio of the width of the classroom to its perimeter.

David :

the perimeter will be 3x+3x+2x+2x=10x, so the ratio is 2x/10x = 2/10 = 1/5

Customer:

38. The ages of three teachers are 48, 28, and 24 years. Fiind, in simplest form, the continued ratio of these ages from oldest to youngest.

David :

it is 24:28:48 or factoring out 4 we get 6:7:12

Customer:

39. A woodworker is fasioning a base for a trophy. He starts with a block of wood whose length is twice its width and whose height is one-half its width. Write, in simplest form, the continued ratio of length to width to height.

David :

it is L:W:H = 2W:W:1/2W = 2:1:1/2 and multiplying by 2 we get 4:2:1

Customer:

Here is the last problem. 40. Taya and Jed collect coins. The ratio of the number of coins in their collections, in some order, is 4 to 3. If Taya has 60 coins in her collection, how many coins could Jed have?

David :

since it is 4:3 then there are 2 options
1) jed has more then it is 60*4/3 = 80
2) jed has less then it is 60*3/4 = 45

Customer:

Thank you so much. It has been a real pleasure working with you. Have a great night.

David :

you are very welcome

Customer:

Just wanted to say Good Night and Thanks before "accepting"

David :

good night

David :

please do not hesitate to request me in the future just begin your post with "For David" and I'll revert immediately if I'm online

Customer:

Will do.