Answer:
Step-by-step explanation:
1: 581
2: 967
3:588
Let x be the unknown amount of child tickets
Let 450 - x be the unknown amount of adult tickets (This is because the total amount subtracted from the child tickets can only be the adult tickets since there are no other tickets)
2x+5(450-x)=1800
(2x because each child ticket cost $2 and same for the adult tickets. Each adult ticket cost $5. So, the sum must be 1800.)
Simplify the equation.
2x+5(450-x)=1800 *Distribute*
2x+2250-5x=1800 *Combine like terms. (2-5=-3)*
-3x + 2250 = 1800 *Move constants and variables to opposite sides*
-2250 -2250
---------------------------
-3x=-450 *Divide by 3 to isolate the variable*
---- ------
-3 -3
x=150
So, there are 150 child tickets. To find adult tickets, just subtract children tickets from the amount of tickets bought (450-150) to get 300 adult tickets sold.
Both systems will have the same value of x's.
Answer:
(3x^2 + 2)(x + 4).
Step-by-step explanation:
3x3 + 12x2 + 2x + 8
3x^2(x + 4) + 2(x + 4) The x + 4 is common to the 2 groups so we have:
(3x^2 + 2)(x + 4).
Answer:
a. 61.92 in²
b. 21.396 ≈ 21.4%
c. $4.71
Step-by-step explanation:
a. Amount of waste = area of rectangular piece of stock - area of two identical circles cut out
Area of rectangular piece of stock = 24 in × 12 in = 288 in²
Area of the two circles = 2(πr²)
Use 3.14 as π
radius = ½*12 = 6
Area of two circles = 2(3.14*6²) = 226.08 in²
Amount of waste = 288 - 226.08 = 61.92 in²
b. % of the original stock wasted = amount of waste ÷ original stock × 100
= 61.92/288 × 100 = 6,162/288 = 21.396 ≈ 21.4%
c. 288 in² of the piece of stock costs $12.00,
Each cut-out circle of 113.04 in² (226.08/2) will cost = (12*113.04)/288
= 1,356.48/288 = $4.71.
