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orange juice a raisin bagel and a cup of coffee cost 3.35 the orange juice will increase 50% and bagels will increase 20% after increase same purchase will cost 4.20, and the orange juice will cost twice as much as coffee. how much was the orange juice, bagel and coffee before increase ​

Respuesta :

Answer:

Orange juice costs 0.90, bagel costs 2 and a cup of coffee costs 0.45.

Step-by-step explanation:

Let x, y and z be the cost of the orange juice, the raisin bagel and the cup of coffee respectively,

Thus, the original cost = x + y + z

∵ the orange juice will cost twice as much as coffee

⇒ x = 2z   ...........(1)

So, the total cost = 2z + y + z = y + 3z,

After increasing the price of orange juice by 50% and the price of bagels by 20%,

New cost = 150% of x + 120% of y + z = 1.5x + 1.2y + z = 3z + 1.2y + z = 1.2y + 4z

According to the question,

y + 3z = 3.35  .............(2)

1.2y + 4z = 4.20  ...........(3)

Equation (3) - 1.2 × equation (2),

4z - 3.6z = 4.20 - 4.02

0.4z = 0.18

⇒ z = 0.45,

From equation (2),

y + 1.35 = 3.35

⇒ y = 2,

From equation (1),

x = 2(0.45) = 0.9

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