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

Answer:

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

Step-by-step 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.