Could someone help me with math?

Question

I just need help with these 3 problems.

1. If the United States imports increased 20% and exports decreased 10% during a certain year, the ratio of imports to exports at the end of the year was how many times the ratio at the beginning of the year?
A) 12/11
B) 4/3
C) 11/8
D) 3/2
E) 2

2. If it takes Mark twice as long to earn $6 as it takes Carl to earn $4, what is the ratio of Mark's pay per hour to Carl's pay per hour?
A) 2:1
B) 3:1
C) 3:2
D) 3:4
E) 4:3

3. The ratio of the arithmetic mean of two numbers to one of the numbers is 3:5. What is the ratio of the smaller number to the larger?
A) 1:5
B) 1:4
C) 1:3
D) 1:2
E) 2:3

Answer 1

1. Problem No. 1 is not ideal in that it does not have dollar amounts for exports and imports at the beginning of the year.
However, we can use the unity rule, saying the exports and imports had a ratio of one to one at the beginning. This means they had the same dollar amounts and a beginning ratio of 1:1.

Therefore, with the 20% increase in imports and 10% decrease in exports, the new ratio of imports to exports will be 1.20/0.90 or 4/3 or 1.33.

The ratio of the new ratio of imports to exports to the old starting ratio will also be 4/3 since the geginning ratio was 1:1.

2. From the problem, we can equate Carl's earning as $4/hr.Then, we can calculate Mark's earning as follows:
$6/2 hrs = $3 per hour. Why do we divide by 2? Because
the problem said that period is twice the time Carl will
have earned $4 (which is one hour for Carl0.

The ratio of Mark's hourly pay to that of Carl's will therefore
be 3/4.

3. We first have to look for the two numbers X and Y whose
mean (arithmetic average) is 3.5. Our assumption is that each number is an integer, i..e, a whole number with no decimals.

Our formula is:

(x + y)/2 = 3.5 the mean.
x+y = 7
Here we can see we have 3 possibilities for x and y:

1 + 6 = 7
3 +4 =7
2 +5 = 7

All these three sets will have an average of 3.5

But, of the six numbers above, only 1 can have ratio
of 3.5:1 to the 3.5 mean.

Therefore, the x and y must be 1 and 6.
Our ratio of the smaller to the bigger no. is therefore:

1/6 or 1:6

Unfortunately, this answer is not among those listed
in the above answers.


I hope I was able to help you somehow. I tried to give explanations to each step I took in my solutions for your guidance. My goal is not to give you the answers, but to guide you how to arrive at them.

Blessings, and have a great day!

Answer 2

1- 20% more = 120% and 10% less = 90% so 120:90 = 4:3
answer B
2- 6 is to 2 as 4 is to 1 so u should divide 6:2= 3 and 4:1=4 and the answer is 3:4 letter D
3- x+y/2 is an arithmetic mean so in this case x+y/2=3... lets call the biggest number as y... so x+5/2=3... x+5=6 and x=1
that makes you choose the answer A) 1:5

I hope u understood the way I´ve posted the answers!
Good luck with your homework

Answer 3

I/E = 1.2/.9 = 4/3

6 = M * 2t
4 = C * t, or t = 4/C. So, 6 = M *2 *4/C or M/C = 6/8 (3:4)

[(x+y)/2]/x = 3/5, so (x+y)/2 = 3x/5, or 5x + 5y = 6x, so
5y = x, and y/x = 1/5 (1:5)

Answer 4

1,
120/90 = 4/3

2.
2hrs = 6/8=3/4

3.
nos = 1,3,5
ratio of the smaller number to the larger= 1:5

Answer 5

1.2/.9 = 12/9= 4/3

(6/2)/4 = 3/4

(5x+3x+z)/3 = 3x
5x+3x+z = 9x
z = x
x/5x = 1/5

Answer 6

1. Export/Import

ratio(beggining)= I/E

At end of year:
I(year end) =1.2I
E(year end) = 0.9E

ratio (year end) =
= ratio of I(year end) to E(year end)
= 1.2I/0.9E

how many times =
= ratio (year end) / ratio (beginning)
= (1.2I/0.9E) / (I/E)
= 1.2/0.9
= 4/3