URGENT MATH DUE IN 1 hour

Question

MIcheal and Dwight went to a candy store. Micheal bought 5 pieces of fudge and 3 pieces of bubblegum for a total of $5.70. Dwight bought 2 pieces of fudge and ten pieces of bubblegum for a total of $3.60 What is the price of one piece of fudge and one piece of bubblegum? Use Systems of equations to solve, either substitution or elimination. EXPLAIN WHY YOU CHOSE TO USE THE METHOD YOU USED AND WHY

Answer 1

Suppose f and b are the prices

5f + 3b = 5.70 (1)

2f + 10b = 3.60 (2)

10f + 6b = 11.40 (3) = 2 (1)

10f + 50b = 18 (4) = 5 (2)

44b = 6.60 (4)- (3)

b = 6.60 / 44 = 0.15

2f = 3.60 - 10b = 2.10

f = 2.10 / 2 = 1.05

f = 1.05

b = 0.15

Answer 2

Hi there,

For easier setup, I'm going to set Fudge's price = F, and Bubblegum's price = B

Ok, so let's follow the question. First, we see Michael bought 5 pieces of fudge and 3 pieces of bubblegum for a total of $5.70. Therefore we have the first equation 5F + 3B = 5.7, 5 pieces of fudge each costs F and 3 pieces of bubblegum each costs B, and he paid $5.7 in total for those things.

Next, let's see what Dwight bought. bought 2 pieces of fudge and ten pieces of bubblegum for a total of $3.60. We get this equation number two, which is 2F + 10B = 3.6, similarly, 2 pieces of fudge each costs F and 10 pieces of bubblegum each costs B, and Dwight paid $3.6 in total for those things.

So at the end, you get this system from the question including two equations:

5F+3B = 5.7  Equation #1

2F+10B = 3.6  Equation #2

Either method would work here. I personally prefer elimination, because it's easier in my opinion. There is not really a reason for preferring one over the other, it is a personal habit thing.

Use Equation #1 multiplied by 2, you will get

10F + 6B = 11.4  Equation #3

Use Equation #2 multiplied by 5

10F+50B = 18  Equation #4

use #4 - #3, the F variable cancelled out and there's only B left (Elimination)

44B = 6.6

B = .15

Plug B= .15 back to any of the equation above to find what F equals to, I used #2, F is 1.05.

Always check your answers by plugging them back to the other equation to make sure the solutions work for this system.

Answer: The price of one piece of fudge is $1.05 and one piece of bubblegum is $.15.

Hope it helps!

Ps: Office is great lol