Question

Jonah and Ermias when to the farmers market. Jonah purchased 14 tomatoes and 13 ears of corn, and Ermias purshased 13 tomatoes and 6 ears of corn. If Jonah spent $83.58 and Ermias spent $61.46, and both people purchased their items from the same vendor, how much did the vendor charge for a single tomato and a single ear of corn?

Answer 1

The vendor charged $34.02 for a single tomato and -$63.47 for a single ear of corn.

Step-by-step explanation:

To find out how much the vendor charged for a single tomato and a single ear of corn, we need to set up a system of equations.

Let's assume the price of a single tomato is represented by 't' and the price of a single ear of corn is represented by 'c'.

We can set up the following equations using the given information:

14t + 13c = $83.58

13t + 6c = $61.46

To solve this system of equations, we can use either the substitution method or the elimination method.

Using the elimination method, we can multiply the second equation by 2 to make the coefficients of t in both equations equal:

26t + 12c = $122.92

Now, we can subtract the second modified equation from the first equation:

(14t + 13c) - (26t + 12c) = $83.58 - $122.92

-12t - c = -$39.34

Next, we can multiply the second equation by 12 to make the coefficients of t in both equations equal:

-12t - c = -$39.34

-12t - 12c = -$737.52

Now, we can subtract the first modified equation from the second modified equation:

(-12t - c) - (-12t - 12c) = -$737.52 - (-$39.34)

11c = -$698.18

Dividing both sides of the equation by 11, we find that c = -$63.47.

Now, we can substitute the value of c into one of the original equations to solve for t:

13t + 6(-$63.47) = $61.46

13t - $380.82 = $61.46

13t = $442.28

Dividing both sides of the equation by 13, we find that t = $34.02.

Therefore, the vendor charged $34.02 for a single tomato and -$63.47 for a single ear of corn.