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 ;)