College Mathematics C17V
Assignment 04,
Mathematics, Problems and Solution
- 1. 73,456 = Seventy three thousand four hundred fifty six
- 2. a. 12,176 ÷ 24 = 507.333
b. 34 • 51 = 3 × 3 × 3 × 3 × 5 = 405
c. √9• √36 = 3 × 6 = 18
d. 12(62-4) = 12 (36-4) = 12 × 32 = 384
e. 7345 • 1000 = 7,345,000
3. a. 1423 + 6234 + 1867 = 9,524 = 9,500
b. 8734 - 2398 = 6,336 = 6,300
4. 7/10 (number of parts shaded/number of equal parts)
5. a. 50/75 = 2/3
b.105/120 = 7/8
6. a. 3/3 ÷ 2/3 = 3/2
b. 4 • 1/12 = 1/3
c. 2/9 • 15/4 • 4/12 = 5/18
d. 1/2÷ 25/4 =2/25
e. 4/3 • 33/5 = 44/5
7. a. The least common multiple (LCM) of 12 and 24 is 24.
b. The least common multiple (LCM) of 7, 9 and 21 is 63.
8. a. 6/7 - 1/3 = 11/21
b. 2/3 + 5/6 + 7/9 = 41/18
c. 15 - 47/9 = 88/9
d. 3/4(5/6 - 1/3) = 3/8
e. (2/5)2 + (1/2)3 = 57/200
9. a. 5.8 + 0.043 + 16.79 = 22.633
b. 20.01 × 11.1 = 222.111
c. 39.4/100 = 0.394
d. 3.32 ÷ 4 × 10 = 8.3
e. 0.2[5.28-(0.7)2] = 0.958
10. 1 teacher = 16.4 students
11. Circumference = 2 • π • radius = 2 • 3.14 • 1.4 = 8.792
12. a. 9/30 = 3/10
b. 3/2 ¿ 3/4= 3 • 4 ¿ 2 • 3 = 12 ¿ 6 = 1/2
13. a. Oranges: $0.96/6 = $0.16 per orange.
$1.20/8 = $0.15 per orange. It is better to buy.
b. Muffins: $10.20/12 = $0.85 per muffin. It is better to buy.
$16.20/18 = $0.90 per muffin.
14. a. n/30 = 9/15
n × 15 = 30 × 9
n = 18
b. 0.1/0.6 = n/12
n × 0.6 = 0.1 × 12
n = 2
15. a. in general 2 out of 11 students are accepted
in fall of 2012: 460 out of x students are accepted in fall of 2012
thus we can set up the proportion
2 : 11 = 460 : x
2/11 = 460/x
2 • x = 460 • 11
x = 2,530 students
2,530 students applied for admission.
b. 3 inches corresponds to 100 miles
15/2 = 7.5 inches apart on the map corresponds to x miles
thus we can set up the proportion
3 : 100 = 7.5 : x
3/100 = 7.5/x
3 • x = 100 • 7.5
x = 250 miles
16. a. 12.3% = 12.3/100 = 0.123
b. 152% = 152/100 = 1.52
17. a. 0.71 = 0.71 (100%) = 71%
b. 0.059 = 0.059 (100%) = 5.9%
18. a. Let’s the number be 'n'
n = 60% • 300
n = 0.6 • 300
n = 180
Thus, 180 is 60% of 300.
b. Let's the number be 'n'
0.2% • n = 24
0.002 • n = 24
n = 24/0.002
n = 12,000
Thus, 0.2% of 12,000 is 24.
19. a. Amount of vinegar = solution of vinegar • ounces of solution
= 40% • 32
= 0.4 • 32
= 12.8
The amount of vinegar in 32 ounces of the solution is 12.8.
b. the price + 7.12% of the price = total amount charged
60 + (7.12/100) • 60 = $64.272
The total amount charged is $64.272.
20. a. P = $450
i = 9% or 0.09
t = 3 months = 3/12 = 1/4 years
A = the total amount due
A = P(1+r•t)
A = 450(1+0.09•1/4)
A = $460.125
The total amount due at the end of 3 months is $460.125.
b. P = $5,000 the principal t = 20 years
r = 0.10 or 10% annual rate
m = 4 compounding period per year
i = 0.10/4 = 0.025 interest rate per period
n = 20 • 4 = 80 total number of compounding periods
A = future value
A = P(1 + i)^n
A = 5000(1 + 0.025)^80
A = $36,047.84
The compound interest factor is A/P = 36,047.84/5,000 = 7,209568.
References
Elayn Martin-Gay (2011). Basic College Mathematics (4th Ed.). Boston: Pearson.
