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 and the price for 2 pounds of tomatoes is
∴ --------- 1
For Betty's purchase:
The price for 2 heads of lettuce is and the price for 3 pounds of tomatoes is
∴ -------- 2
Now, there are 2 equations and 2 unknowns.
Multiply equation 1 by 3 and equation 2 by -2. This gives,
Add the above two equations. This gives,
Now, plug in 0.69 for in equation 1, we get:
∴ and
Therefore, the price for a head of lettuce is $ 0.69 and price for a pound of tomatoes is $ 0.99.