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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.
A. What was the cost of a glass of orange juice before the increase?
B. what was the cost of a raisin bagel before the increase?
C. what was the cost of a cup of coffee before the increase?

Respuesta :

Answer:

Juice $0.6

Bagel $1.5

Coffee $0.3

Step-by-step explanation:

The original price is $2.40 for an orange juice (x), raisin bagel (y) and a cup of coffee(z).

The prices of the orange juice will increase by 50%:

[tex]=x+0.5x=1.5x[/tex]

The price of bagels will increase by 20%:

[tex]=y+0.2x=1.2x[/tex]

The total price of everything is $3.00.

The orange juice will cost twice as much as coffee:

[tex]x=2z[/tex]

We have the following equations:

[tex]x+y+z=2.40[/tex]

[tex]1.5x+1.2y+z=3[/tex]

[tex]x=2z[/tex]

We have 3 equations and 3 unknowns:

Solve through substitution of x=2z into both equations:

[tex]1.5x+y=2.40[/tex]

[tex]2x+1.2y=3[/tex]

Therefore before increase. Use equation before increase to solve z and not x=2z because this is after the increase.

[tex]x=0.6[/tex]

[tex]y=1.5[/tex]

[tex]z=0.3[/tex]