Question

Orange​ juice, a raisin​ bagel, and a cup of coffee from​ Kelly's Koffee Kart cost a total of ​$2.40. Kelly posts a notice announcing​ that, effective the following​ week, the price of orange juice will increase​ 50% and the price of bagels will increase​ 20%. After the​ increase, the same purchase will cost a total of ​$3.00​, and the orange juice will cost twice as much as coffee. Find the price of each item before the increase.

Answer 1

Answer:

orange juice 0.80 dollar

Bagel 1 dollar

coffe 0.60 dollar

Explanation:

We construct the equation system:

$\left \{ {A+B+C = 2.40} \atop {1.5A+1.2B+C = 3}} \right.$

We subtract one from another to get an expression without C:

1.5A+1.2B+C - (A+B+C) = 3   -  2.40

0.5A + 0.2B  = 0.6

Then, we solve in the first part to express B as an expression of A

considering the coffe is worth half of the new cost of A

C = 1.5A / 2 = 0.75A

A + B + C = 2.40

A + B + 0.75A = 2.40

B = 2.40 - 1.75A

And now we replace in the other expression to get A:

0.5A + 0.2(2.40 - 1.75A) = 0.6

0.5A - 0.35A + 0.48 = 0.60

0.15A = 0.12

A = 0.12/0.15 = 0.8

Now we solve for C:

C = 0.75A = 0.6

Last, for B:

A + B + C = 2.40

0.8 + B + 0.6 = 2.40

B = 2.40 - 0.8 - 0.6 = 1