Question

Joan bought 3 Heads of lettuce and 2 pounds of tomatoes for $4.05. Betty bought two heads of lettuce and 3 pounds of tomatoes for $4.35 at the same store. What Are the prices for a head of lettuce and a pound of tomatoes?

Answer 1

Price for a head of lettuce is $ 0.69 and price for a pound of tomatoes is $ 0.99.

Explanation:

Let x be the price for a head of lettuce and y be the price for a pound of tomatoes.

For Joan's purchase:

The price for 3 heads of lettuce is
`3x` and the price for 2 pounds of tomatoes is
`2y`

∴
`3x+2y=4.05` --------- 1

For Betty's purchase:

The price for 2 heads of lettuce is
`2x` and the price for 3 pounds of tomatoes is
`3y`

∴
`2x+3y=4.35` -------- 2

Now, there are 2 equations and 2 unknowns.

Multiply equation 1 by 3 and equation 2 by -2. This gives,

`9x+6y=12.15`

`-4x-6y=-8.70`

Add the above two equations. This gives,

`9x-4x=12.15-8.70\\ 5x=3.45\\ x= 0.69`

Now, plug in 0.69 for
`x` in equation 1, we get:

`3(0.69)+2y=4.05\\ 2.07+2y=4.05\\ 2y=4.05-2.07\\ 2y=1.98\\ y = 0.99`

∴
`x=0.69` and
`y=0.99`

Therefore, the price for a head of lettuce is $ 0.69 and price for a pound of tomatoes is $ 0.99.