Question

The total cost of buying two potatoes and a half pound of hamburger at the grocery store is $3.00. Lisa buys one potato and two pounds of hamburger and pays $8.50. Find the price for each potato and each pound of hamburger.

doing test rn need help asap

Answer 1

After setting up two equations based on the given information and solving them, we find that the price of each potato is $0.50 and the price per pound of hamburger is $4.00.

Step-by-step explanation:

Price of Each Potato and Pound of Hamburger

Let's denote the price of each potato as P and the price per pound of hamburger as H. From the given information, we have two equations:

1. 2P + 0.5H = $3.00 (two potatoes and a half pound of hamburger)
2. P + 2H = $8.50 (one potato and two pounds of hamburger)

Now, let's solve this system of equations step by step:

1. Multiply the first equation by 2: 4P + H = $6.00.
2. Subtract the second equation from the result of step 1: (4P + H) - (P + 2H) = $6.00 - $8.50, which simplifies to 3P - H = -$2.50.
3. Now, solve for P: 3P = H - $2.50. From the adjusted first equation, we get H = $6.00 - 4P. Substitute H in the third equation: 3P = ($6.00 - 4P) - $2.50. Thus, 3P = $3.50 - 4P, which leads to 7P = $3.50, and P = $0.50.
4. Having found P, substitute it back into the first equation: 2($0.50) + 0.5H = $3.00. This simplifies to $1.00 + 0.5H = $3.00. Therefore, 0.5H = $2.00, and H = $4.00 per pound.

In conclusion, the price of each potato is $0.50 and the price per pound of hamburger is $4.00.