1. ![Expression: 3(5a + 2)](/tpl/images/0911/8972/6f706.png)
2. ![Total\ charges = 6.25(s+g)](/tpl/images/0911/8972/84df9.png)
3. ![Total = 65x + 18 + 65y](/tpl/images/0911/8972/5f5be.png)
4. Michelle
5. 20 friends
6. Thor
8. ![x\leq 5](/tpl/images/0911/8972/c232d.png)
9. ![x + x + 5 = 32](/tpl/images/0911/8972/b8960.png)
10.
so: ![n \leq 5](/tpl/images/0911/8972/4d56d.png)
11.
So: ![n \leq 6](/tpl/images/0911/8972/11387.png)
12.
so ![p \leq 4](/tpl/images/0911/8972/00017.png)
Step-by-step explanation:
1. Given
![Expression: 15a + 6](/tpl/images/0911/8972/5516a.png)
Required
Determine the equivalent expression
![Expression: 15a + 6](/tpl/images/0911/8972/5516a.png)
Expand:
![Expression: 3 * 5a + 3 * 2](/tpl/images/0911/8972/5bd21.png)
Factorize:
![Expression: 3(5a + 2)](/tpl/images/0911/8972/6f706.png)
Hence, the equivalent expression of the given expression is ![3(5a + 2)](/tpl/images/0911/8972/239b0.png)
2.
Given
![Charges = \$6.25](/tpl/images/0911/8972/e5ece.png)
s = seventh grade students
g = eight grade students
Required
Determine the total charges
First, we need to calculate the total number of charges:
![Total=s+g](/tpl/images/0911/8972/83f10.png)
![Total\ charges = Charges * Total](/tpl/images/0911/8972/c1b8c.png)
![Total\ charges = 6.25(s+g)](/tpl/images/0911/8972/84df9.png)
3. Given
Ken
![Duration = x\ weeks](/tpl/images/0911/8972/ce8ca.png)
![Extra\ Earnings = \$18](/tpl/images/0911/8972/34743.png)
![Weekly\ Earnings = \$65](/tpl/images/0911/8972/21494.png)
Paul
![Weekly\ Earnings = \$65](/tpl/images/0911/8972/21494.png)
![Duration = y\ weeks](/tpl/images/0911/8972/922ab.png)
Ken's total charges is:
![Weekly\ Earnings * Duration + Extra\ Earnings](/tpl/images/0911/8972/f670a.png)
![65 * x + 18](/tpl/images/0911/8972/b5588.png)
![65x + 18](/tpl/images/0911/8972/86617.png)
Paul's total charges is:
![Weekly\ Earnings * Duration](/tpl/images/0911/8972/06b58.png)
![65 * y](/tpl/images/0911/8972/a755e.png)
![65 y](/tpl/images/0911/8972/1b061.png)
![Total = Ken + Paul](/tpl/images/0911/8972/4aa91.png)
![Total = 65x + 18 + 65y](/tpl/images/0911/8972/5f5be.png)
4.
To calculate the percentage, we simply divided the number of pop albums by the total number of albums.
For Michelle.
![\%Pop = \frac{33}{60} * 100\%](/tpl/images/0911/8972/4bd84.png)
![\%Pop = \frac{3300\%}{60}](/tpl/images/0911/8972/5e268.png)
![\%Pop = 55\%](/tpl/images/0911/8972/f76ba.png)
For Sasha
![\%Pop = \frac{36}{78} * 100\%](/tpl/images/0911/8972/c9247.png)
![\%Pop = \frac{3600\%}{78}](/tpl/images/0911/8972/c1572.png)
![\%Pop = 46.2\%](/tpl/images/0911/8972/fef38.png)
For Kat:
![\%Pop = \frac{40}{89} * 100\%](/tpl/images/0911/8972/cc6f3.png)
![\%Pop = \frac{4000\%}{89}](/tpl/images/0911/8972/714bc.png)
![\%Pop = 44.9\%](/tpl/images/0911/8972/e1265.png)
For Monica:
![\%Pop = \frac{24}{59} * 100\%](/tpl/images/0911/8972/bd0d6.png)
![\%Pop = \frac{2400\%}{59}](/tpl/images/0911/8972/a771b.png)
![\%Pop = 40.7\%](/tpl/images/0911/8972/8dd99.png)
From the calculation above, Michelle has the highest percentage of Pop music
5.
![People = 80](/tpl/images/0911/8972/593cf.png)
![Fortnite = 0.55](/tpl/images/0911/8972/8eed5.png)
![Among\ Us = 30\%](/tpl/images/0911/8972/91df1.png)
Required
Determine number of friends that prefer fortnite more than among us
First, we need to calculate the number of people that prefer Fortnite.
![Fortnite = 0.55 * 80](/tpl/images/0911/8972/44b6d.png)
![Fortnite = 44](/tpl/images/0911/8972/7910a.png)
Next, we need to calculate the number of people that prefer Among Us.
![Among\ Us = 30\% * 80](/tpl/images/0911/8972/621bb.png)
![Among\ Us = 24](/tpl/images/0911/8972/25fa3.png)
The difference is:
![Difference = 44 - 24](/tpl/images/0911/8972/203ac.png)
![Difference = 20](/tpl/images/0911/8972/b4fa8.png)
Hence, 20 more people preferred Fortnite to Among Us
6.
![Hulk = 0.25](/tpl/images/0911/8972/47db0.png)
![Iron\ Man = 12](/tpl/images/0911/8972/ca987.png)
![Thor = 35\%](/tpl/images/0911/8972/dfc0e.png)
Captain America cleaned the rest
![Total = 60](/tpl/images/0911/8972/6bd1e.png)
Number of cities by each is:
![Hulk = 0.25 * 60](/tpl/images/0911/8972/c3f74.png)
![Hulk = 15](/tpl/images/0911/8972/9cb4b.png)
![Iron\ Man = 12](/tpl/images/0911/8972/ca987.png)
![Thor = 35\%](/tpl/images/0911/8972/dfc0e.png)
![Thor = 35\% * 60](/tpl/images/0911/8972/3828b.png)
![Thor = 21](/tpl/images/0911/8972/bb06f.png)
![Captain\ America = 60 - 15 -12 - 21](/tpl/images/0911/8972/f1cac.png)
![Captain\ America = 12](/tpl/images/0911/8972/c56e5.png)
By comparison, Thor cleaned the highest number of cities
7. This question is not clear
![Total = \$70](/tpl/images/0911/8972/d9ee3.png)
![Glass = \$30](/tpl/images/0911/8972/1345d.png)
![Each\ Cape = \$8](/tpl/images/0911/8972/d9044.png)
Let the number of cape be x.
We have that:
![8 * x + 30 \leq 70](/tpl/images/0911/8972/ee8fd.png)
![8 x +\leq 70 - 30](/tpl/images/0911/8972/5fa7b.png)
![8 x +\leq 40](/tpl/images/0911/8972/8ebc0.png)
![x\leq 5](/tpl/images/0911/8972/c232d.png)
9.
Let the first number be x and the second be y
![x + y = 32](/tpl/images/0911/8972/a2f1f.png)
![y = x + 5](/tpl/images/0911/8972/12a19.png)
Substitute x + 5 for y in the first equation
![x + x + 5 = 32](/tpl/images/0911/8972/b8960.png)
10.
![Savings = \$9](/tpl/images/0911/8972/4aee8.png)
Earnings = $7 per hous
Total = $44
The inequality is:
![7 * n + 9 \leq 44](/tpl/images/0911/8972/ec495.png)
![7n + 9 \leq 44](/tpl/images/0911/8972/529ab.png)
![7n \leq 44 - 9](/tpl/images/0911/8972/6615b.png)
![7n \leq 35](/tpl/images/0911/8972/1fcbd.png)
![n \leq 5](/tpl/images/0911/8972/4d56d.png)
11.
Earnings = $40
Extra = $5 per lasso
Total Earnings = At least $70 daily
The inequality is:
![40 + 5n \leq 70](/tpl/images/0911/8972/a3b99.png)
![5n \leq 70 - 40](/tpl/images/0911/8972/6fc42.png)
![5n \leq 30](/tpl/images/0911/8972/e50bc.png)
![n \leq 6](/tpl/images/0911/8972/11387.png)
12.
![Each\ Cake = \$0.01](/tpl/images/0911/8972/c19a8.png)
per order
--- maximum
The inequality is:
![10.01 * p + 9.96 \leq 50](/tpl/images/0911/8972/10963.png)
![10.01 p + 9.96 \leq 50](/tpl/images/0911/8972/ee2f2.png)
![10.01 p \leq 50 - 9.96](/tpl/images/0911/8972/3fc59.png)
![10.01 p \leq 40.04](/tpl/images/0911/8972/e638e.png)
![p \leq 4](/tpl/images/0911/8972/00017.png)