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In free math answers, these are the questions asked by the students to show it in step-by-step solution.
1. In a group of cows and chickens, the number of legs was 14 more than twice the number of heads. The number of cows was:
(a) 5, (b) 7, (c) 10, (d) 12, (e) 14
Solution:
Let the number of cows be x and their legs be 4x.
Let the number of chicken be y and their legs be 2x.
Total number of legs = 4x + 2y.
Total number of heads = x + y.
The number of legs was 14 more than twice the number of heads.
Therefore, 2 × (x + y) + 14 = 4x + 2y.
or, 2x + 2y + 14 = 4x + 2y.
or, 2x + 14 = 4x [subtracting 2y from both sides].
or, 14 = 4x – 2x [subtracting 2x from both sides].
or, 14 = 2x.
or, x = 7 [dividing by 2 on both sides].
Therefore, the number of cows = 7.
Answer: (b)
4. A circle of radius 10 inches has its center at the vertex C of an
equilateral triangle ABC and passes through the other two vertices. The
side AC extended through C intersects the circle at D. The number of
degrees of angle ADB is:
(a) 15, (b) 30, (c) 60, (d) 90, (e) 120
8. A 7-in. pizza costs $8 and a 14-in. pizza costs $20. Tommy says
the smaller pizza is a better buy because the larger pizza is twice as
big and more than twice as expensive. Do you agree with his reasoning?
If not, explain why not.
Solution:
No, a pizza looks like a circle.
And we know that area of a circle depends on the radius.
So, we can clearly say that area of a circle is proportional to the square of the diameter.
Similarly, the cost a pizza depends on its area not its diameter.
9. Suppose that Jody drove 80 miles in 2 hours. Dividing 80 by 2
tells us how many miles Jody drove in each hour. The units for this rate
are miles per hour (mi/hr). If we divide 2 by 80 what information would
this give us? Give an interpretation of the rate. What units would be
used for this rate?
Solution:
We know that, speed = distance/time.
When total distance is divided by total time we get the speed.
Here, speed = distance covered in 1 hour.
According to the question,
Total distance 80 miles divided by total time 2 hours = 80/2.
miles/hour = 40 mile/hour.
Therefore, Jody drove 40 miles in 1 hour.
But if we divide total time by total distance then, we get time taken to cover 1 mile.
Similarly, if we divide 2 by 80 then, we get time taken to cover 1 mile.
Therefore, unit used for this case = hours/mile.
10. 19/6 = 4/27. Which method did you use to determine whether this proportion is true or false?
Solution:
19/6 = 4/27.
Cross multiplication:
19 × 27 = 513.
6 × 4 = 24.
We see that 513 are not equal to 24.
Therefore, we determine 19/6 = 4/27 is not proportion so, the answer is false.
11.
On Thursday Mabel handled 90 transactions. Anthony handled 10% more
transactions than Mabel, Cal handled 2/3rds of the transactions that
Anthony handled, and Jade handled 16 more transactions than Cal. How
much transactions did Jade handled?
Solution:
Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 16 more transactions than Cal.
Jade = 66 + 16
= 82
Jade handled = 82 transactions.
Answer: 82
12. If a man buys 20 lollipops for $90 and sold them for $2 dollars determine his loss.
Solution:
Cost of 20 lollipops = $90
Sold each lollipop for $2
So he sold 20 lollipops for $(20 × 2) = $40
Loss = $(90 – 40) = $50
Therefore, loss = $ 50.
13 . If C is a whole number, C+1 is a whole number after that. If A is a whole number, what is a whole number before that?
Solution:
We know that the number ‘0’ together with the natural numbers gives us the numbers 0, 1, 2, 3, 4, 5, …………… which are called whole numbers.
If A is a whole number and it is greater than 0 then the whole number before that is A – 1, which will always be a whole number.
Again,
when A is a whole number and it is equal to 0 then the whole number
before that is A – 1 which means 0 – 1 = -1, which is not a whole
number.
Therefore, if A is a whole number then the number before that will not always be a whole number.
14. Solve and leave answer in fraction
- (2-5/4)/9
Solution:
Answer: -1/12
15. Divide the cancelling out all common factors
Solution:
-((1-13/8)/10/24)
Answer: 3/2
16. The annual cost of owning and operating a car, C dollars, is a linear function of the distance, d kilometers, it is driven.
c = md + b
The cost is $4600 for 10 000 km and $9100 for 25 000 km.
(a) Determine the values of m and b.
(b) Write c as a function of d.
Solution:
(a)
c = md + b
The cost is $ 4600 for 10 000 km
4600 = m (10 000) + b
10 000 m + b = 4600
b = -10 000 m + 4600 ------- (i)
The cost is $ 9100 for 25 000 km
9100 = m (25 000) + b
9100 = 25 000 m + b
25 000 m + b = 9100
b = -25 000 m + 9100 --------- (ii)
From equation (i) and (ii) we get;
-10 000 m + 4600 = -25 000 m + 9100
-10 000 m + 25 000 m = 9100 – 4600
15 000 m = 4500
m = 4500/15 000
m = 3/10
m = 0.3
Now, put the value of m = 0.3 in equation (i) we get;
b = -10 000 (0.3) + 4600
b = -3000 + 4600
b = 1600
Answer: m = 0.3 and b = 1600
(b) c = md + b
m = 0.3
b = 1600
c = 0.3d + 1600
Answer: c = 0.3d + 1600
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