The quotient of an integer and a decimal number is never an integer.

23) Here's what we know:

a + c = 11

22a + 15c = 228

By moving either a or c over in our first equation, we can create a substitution problem:

c = 11 - a

22a + 15(11 - a) = 228

22a + 165 - 15a = 228

7a +165 = 228

7a = 63

a = 9

So 9 adults.

c = 11 - a

c = 11 - 9

c = 2

And 2 children

ccc

Now to check our

22 * 9 + 2 * 15 = 228

198 + 30 = 228

228 = 228

24) six vehicles, buses and vans:

b + v = 6

b = 6 - v

Question: Are the drivers included in the 142 total

persons?

51b + 10v = 142

51(6-v) + 10v = 142

-306- 51v + 10v = 142

-41v = 142-306

-41v = - 164

v = 0.25

b = 1.7561

2 buses and 4 vans: 2(52)+4(11) = 148 person

capacity: 142 attendees and 6 drivers.

2 buses and 4 vans: 2(52)+4(11) = 148 person

capacity: 142 attendees and 6 drivers.

Note: each bus holds 52 persons

51 passengers and the driver

Each van holds 11 persons by same logic. 10+driver

25) NOTE: Right triangle with two acute angles; <A and <B

Step 1:

<A = 4x

<B = x

<C = 90 (right angle)

Explanation to step 1:

One acute angle is 4 times the other; 4x

(Either <A or <B; let's pick <B)

Step 2:

180 = A + B + C

180 = 4x + x + 90

Note that to step 2:

The angles in a triangle always equal to 180 degrees.

Step 3:

180 = 4x + x

Subtract 90 from both sides to get...

90 = 4x + x

Combine like terms to get...

90 = 5x

Divide both sides by 5 to get...

18 = x

Note that in step 3:

Solve for x.

Step 5: (this help you get the solution to your problem)

x = 18 = <B

4x = 4(18) = 72 = <A

Note that after completing all the steps will lead up to step 5, then after step 5 You would get the answer to your problem.

ANSWER:

18 degrees, 72 degrees

Hope this helps and I'm sorry it was an 3 weeks late answer but I do hope that my step by step will help you with more problems like this. And if you think this was a reward of brainliest I would much appreciate it but if not I'm still happy I helped Good Luck ;)