Answer: price of soda (a) = $2 and price of popcorn (b) = $0.5
Step-by-step explanation:
Let's denote soda = a and popcorn = b
Kaylin bought a soda and two popcorn, writing out an equation for this would be
a + 2b = $3...........equation (i)
And her brother bought 3 sodas and 1 popcorn.
3a + b = $6.50..........equation (ii)
From equation (i),
a + 2b = 3
Making a the subject of formula,
a = 3 - 2b......equation (iii)
Using substitution reaction, put equation (iii) into equation (ii)
3(3 - 2b) + b = $6.50
9 - 6b + b = 6.50
9 - 5b = 6.50
Collecting like terms,
5b = 9 - 6.50
Divide both sides by 5,
b = 5.
Put b = 5 into equation (i)
a + 2(0.5) = 3
a + 1 = 3
a = 2
Therefore, the price of soda is $2 per one and $0.5 for each popcorn.
Divide 24 by 3, and you will get the answer of 8.
You set the expressions equal to each other since they are congruent, then solve.
5x + 24 = 9x - 17
First subtract 24 from both sides to get
5x = 9x - 41
The subtract 9x from both sides to get
-4x = -41
Then divide both sides by -4 to get
x = 41/4 or as a decimal x = 10.25
Let's prove triangle DEF:
10/7=1.428571429 different to 1.5=9/6, then triangle DEF is not similar to triangle ABC
Let's prove triangle GHI:
3.5/7=0.5=3/6, then triangle GHI is similar to triangle ABC
Answer: Option B. GHI
