Answer:
$3 and $2
Step-by-step explanation:
let p represent popcorn and d drinks , then
2p + 3d = 12 → (1)
3p + 5d = 19 → (2)
multiplying (1) by 3 and (2) by - 2 and adding will eliminate p
6p + 9d = 36 → (3)
- 6p - 10d = - 38 → (4)
add (3) and (4) term by term to eliminate p
0 - d = - 2
- d = - 2 ( multiply both sides by - 1 )
d = 2
substitute d = 2 into either of the 2 equations and solve for p
substituting into (1)
2p + 3(2) = 12
2p + 6 = 12 ( subtract 6 from both sides )
2p = 6 ( divide both sides by 2 )
p = 3
Popcorn costs $3 and a drink costs $2
if 4 to 6 then 16 to 24, but if its 4 minus 6, its -8 cups
Answer + Explanation + Theory
When a number is divided by a number it results in a quotient and a remainder
E.g. 9 / 4 = 2 remainder 1
9 is the dividend
4 is the divisor
2 is the quotient
1 is the remainder
Same way when a polynomial is divided by a linear expression
E.g.
Ax^2 + bx + c / (x-b) = (x+a) + r
Which can be rearranged to
ax^2 + bx + c = (x+a)(x-b) + r
When x = - a or b, only the remainder is left since either (x+a)(x-b) is 0.
If x = - a or b is substituted into the polynomial and the value is 0 then there is no remainder,
This would suggest (x+a) or (x-b) are factors of the polynomial.
Now apply this logic to these questions
1. Let’s assume (x-4) is a factor, this would mean that when x=4 is substituted into the polynomial the answer would be 0.
This is the case, therefore the remainder is 0.
2. Having seen the logic above (applied using the remainder and factor theorem) the linear expression is a factor of the polynomial.
