SOLUTION: Craig and Leticia go to the store together to buy tomatoes to make salsa. Together they paid 14.62 dollars for tomatoes and peppers. Craig paid 2.38 dollars more for his tomatoes

Question 945063: Craig and Leticia go to the store together to buy tomatoes to make salsa. Together they paid 14.62 dollars for tomatoes and peppers. Craig paid 2.38 dollars more for his tomatoes and peppers than leticia paid for hers . Craig's recipe calls for 10 tomatoes and 6 peppers. Leticia's recipe calls for 8 tomatoes and 4 peppers.
How much does a tomatoe and pepper cost?

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
The description refers to counting each tomato and pepper.

t for price of tomato;
p for price of pepper.

CRAIG:
10 tomatos and 6 peppers.
, how many dollars he spent for his items.
He paid $2.38 more than Leticia paid, so .......

C for Craigs payment, L for Leticia's payment,
This system of equations will help find the amount that each paid for his or her items.

LETICIA:
8 tomatos and 4 peppers.
, how much she paid for her items.

Using the payment expressions for Craig and Leticia, and keeping the payment variables L and C, we have the system:

These two separate systems are really ONE system of four equations in four unknowns, but easier to solve the C & L system first; and then use the values found for the items cost system to solve for and .

I did not finish solving this, only presented a logical process and described it. ( )
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

Craig and Leticia go to the store together to buy tomatoes to make salsa. Together they paid 14.62 dollars for tomatoes and peppers. Craig paid 2.38 dollars more for his tomatoes and peppers than leticia paid for hers . Craig's recipe calls for 10 tomatoes and 6 peppers. Leticia's recipe calls for 8 tomatoes and 4 peppers.
How much does a tomatoe and pepper cost?

Let amount Leticia paid be L
Then Craig paid: L + 2.38
We then get: L + L + 2.38 = 14.62
2L + 2.38 = 14.62
2L = 14.62 � 2.38
2L = 12.24
L, or amount Leticia paid = , or $6.12
Amount Craig paid: 6.12 + 2.38, or $8.50
Let cost of 1 tomato, and 1 pepper be T, and P, respectively
Then we get: 10T + 6P = 8.5 ------- eq (i)
Also, 8T + 4P = 6.12______4(2T + P) = 4(1.53)_____2T + P = 1.53 ------- eq (ii)
Solve these 2 equations to determine cost of 1 tomato, and 1 pepper
You should get: , respectively
You can do the check!!
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