April sold 75 tickets to the school Christmas play and collected $495. If adult tickets cost $8 and children tickets were $5 how
1 answer:
40 adult tickets were sold and 35 children tickets were sold
<em><u>Solution:</u></em>
Let "a" be the number of adult tickets sold
Let "c" be the number of children tickets sold
Cost of 1 adult ticket = $ 8
Cost of 1 children ticket = $ 5
<em><u>Given that April sold 75 tickets to the school Christmas play and collected $495</u></em>
Number of tickets sold = 75
number of adult tickets sold + number of children tickets sold = 75
a + c = 75 ----- eqn 1
<em><u>Given that April collected $495</u></em>
Thus we can frame a equation as:
number of adult tickets sold x Cost of 1 adult ticket + number of children tickets sold x Cost of 1 children ticket = $ 495
8a + 5c = 495 ----- eqn 2
<em><u>Let us solve eqn 1 and eqn 2 to find values of "a" and "c"</u></em>
From eqn 1,
a = 75 - c ---- eqn 3
Substitute eqn 3 in eqn 2
8(75 - c) + 5c = 495
600 - 8c + 5c = 495
-3c = 495 - 600
-3c = - 105
<h3>c = 35</h3>Substitute c = 35 in eqn 3
a = 75 - 35
<h3>a = 40</h3>Thus 40 adult tickets were sold and 35 children tickets were sold
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Answer: The correct answer is:
____________________________________________
→ " 0.00032 " ; or, write as: " " .
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Step-by-step explanation:
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Method 1)
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(0.2)⁵ = ? ;
Note: " 0.2 " = 2/10 = (2÷2) / (10÷2) = 1/5 .
→ (0.2)⁵ = (1/5)⁵ = (1⁵) / (5)⁵ = ? ;
Note: 1⁵ = 1 × 1 × 1 × 1× 1 = 1 ;
Note: 5⁵ = 5 × 5 × 5 × 5 × 5 ;
= (5 × 5) × 5 × 5 × 5 ;
= (25) × 5 × 5 × 5 ;
= (25 × 5) × 5 × 5 ;
= 125 × 5 × 5 ;
= (125 × 5) * 5 ;
= (625 ) × 5 ;
= 3125 .
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→ (0.2)⁵ = (1/5)⁵ = (1⁵ / 5⁵) = .
___________________________________________
Method 2)
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(0.2)⁵ = 0.2 × 0.2 × 0.2 × 0.2 × 0.2 ;
= (0.2 × 0.2) × 0.2 × 0.2 × 0.2 ;
= (0.04) × (0.2) × (0.2) × (0.2) ;
= (0.04 * 0.2) × 0.2 × 0.2 ;
= (0.008) × 0.2 × 0.2 ;
= (0.008) × (0.2 × 0.2) ;
= (0.008) × (0.04) ;
(0.2)⁵ = 0.00032
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Now, just for curiosity, let us see if the values obtained using
both "Method 1" and "Method 2" are equal:
=? 0.00032 ?? ;
→ (1 ÷ 3125) =? 0.00032 ?? ; Yes!
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Also, check work using calculator:
____________________________________________
(0.2)⁵ = 0.00032 . Yes!
____________________________________________
The correct answer is:
____________________________________________
" 0.00032 " ; or, write as: " " .
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Answer:
x=147°
Step-by-step explanation:
1. Analyze: The angle opposite to the 33 degree angle is 33 degrees because they are vertical angles.
2. Make an equation: The sum of all four angles (x, the angle opposite of x, the 33 degree angle, and the angle opposite of the 33 degree angle) is 360°. Therefore the equation would be (33°x2)+2x= 360°.
3. Solve for x:
a. Multiply 33 by 2
66+2x=360
b. Subtract 66 from both sides
66+2x=360
-66 -66
2x=294
c. Divide both sides by 2
x=147
4. Remember to add your label- the degree sign (°)
x=147°