Question

Orange juice, a raisin bagel, and a cup of coffee from Kelly's Koffee cost a total of $3.25. 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 $4.05, and the orange juice will cost twice as much as coffee. Find the price of each item before the increases.1.) What was the cost of a glass of orange juice before the increases? [___]2.) What was the cost of a raisin bagel before the increases? [___]3.) What was the cost of coffee before the increases? [__]

Answer 1

Let the price of Orange juice be x, a raisin bagel be y and a cup of coffee be z.

The equation for cost of orange juice, a raisin bagel and a cup of coffee is,

`x+y+z=3.25`

The cost equal after increase in price of orange juice and bagels is,

`1.5x+1.2y+z=4.05`

The orange juice is twice as much as coffee means,

`\begin{gathered} 1.5x=2z \\ z=0.75x \end{gathered}`

Substitute 0.75x for z in the equations to obatin the equation in x and z varaible.

`\begin{gathered} x+0.75x+y=3.25 \\ 1.75x+y=3.25 \\ y=3.25-1.75x \end{gathered}`
`\begin{gathered} 1.5x+1.2y+0.75x=4.05 \\ 2.25x+1.2y=4.05 \end{gathered}`

Substitute the value of y in equation to obtain the value of x.

`\begin{gathered} 2.25x+1.2\cdot(3.25-1.75x)=4.05 \\ 0.15x=0.15 \\ x=1 \end{gathered}`

Substitute 1 for x in equation z = 0.75x to determine the value of z.

`\begin{gathered} z=0.75\cdot1 \\ =0.75 \end{gathered}`

Substitute 1 for x in equation y = 3.25 - 1.75x to obtain the value of y.

`\begin{gathered} y=3.25-1.75\cdot1 \\ =3.25-1.75 \\ =1.5 \end{gathered}`

Answer:

1. The cost of a glass of orange juice before increase is $1.

2. The cost of a raisin bagen before the increase is $1.5.

3. The cost of coffee before the increase is $0.75.