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

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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