chase and sara went to the candy store. chase bought 5 pieces of fudge and 3 pieces of gum for 5.70. sara bought 2 pieces of fudge and 10 pieces of gum for 3.60. determne the cost of 1 piece of fudge and 1 piece of gum

Let, the cost of 1 piece of fudge = x
Cost of a gum = y

System of equations: 5x + 3y = 5.70
2x + 10y = 3.60

Multiply 1st equation by 2, and second by 5,
New equations: 10x + 6y = 11.40
10x + 50y = 18

Now, subtract 1st from 2nd,
44y = 6.60
y = 6.60 / 44
y = 0.15

Substitute it in second equation,
2x + 10(0.15) = 3.60
2x = 3.60 - 1.5
x = 2.10 / 2
x = 1.05

In short, Cost of a Fudge = $1.05 & Cost of a gum = $0.15

Hope this helps!

adioabiola adioabiola · Answer 2 · 2021-10-12T12:26:19+02:00

The cost of each piece of fudge, x is $1.05 and cost of each piece of gum, y = $0.15

let

cost of each piece of fudge = x

cost of each piece of gum = y

The equation:

5x + 3y = 5.70 (1)

5x + 3y = 5.70 (1)2x + 10y = 3.60 (2)

multiply (1) by 2 and (2) by 5

10x + 6y = 11.4 (3)

10x + 50y = 18 (4)

subtract (3) from ((4) to eliminate x

44y = 6.6

divide both sides by 44

y = 6.6/44

y = 0.15

substitute y = 0.15 into (1)

5x + 3y = 5.70 (1)

5x + 3(0.15) = 5.70

5x + 0.45 = 5.70

5x = 5.70 - 0.45

5x = 5.25

divide both sides by 5

x = 5.25 / 5

x = 1.05

Therefore, the cost of each piece of fudge, x is $1.05 and cost of each piece of gum, y = $0.15