Question

1. on average, 8 potatoes cost $1.50 at a farmers market. fernando needs 22 potatoes.

a. estimate the cost of 22 potatoes. (remember that estimation is not the same as actually solving) explain your estimation.
b. how much will it cost fernando to buy 22 potatoes? how does this compare to your estimate?
c. how many potatoes could fernando buy with $7?
d. what is the cost per potato?

Explanation:

Step1: Find cost per potato for estimation

Round 8 potatoes for $1.50$ to 8 potatoes for $1.60$. Then cost per potato is $\frac{1.60}{8}= 0.2$ dollars.

Step2: Estimate cost of 22 potatoes

$22\approx20$, so estimated cost is $20\times0.2 = 4$ dollars.

Step3: Find actual cost per potato

The actual cost per potato is $\frac{1.50}{8}=0.1875$ dollars.

Step4: Find actual cost of 22 potatoes

$22\times0.1875 = 4.125$ dollars. The actual cost is slightly higher than the estimate.

Step5: Find number of potatoes with $7$ dollars

Let the number of potatoes be $n$. Then $n=\frac{7}{0.1875}=\frac{7}{\frac{3}{16}}=7\times\frac{16}{3}=\frac{112}{3}\approx37.33$. So Fernando can buy 37 potatoes.

Step6: State cost per potato

The cost per potato is $\frac{1.50}{8}=0.1875$ dollars.

Answer:

a. The estimated cost of 22 potatoes is $4$ dollars. The estimation was done by rounding 8 - potato cost to $1.60$ (easier to divide) and 22 potatoes to 20 potatoes.
b. It will cost Fernando $4.125$ dollars to buy 22 potatoes. The actual cost is slightly higher than the estimate.
c. Fernando can buy 37 potatoes with $7$ dollars.
d. The cost per potato is $0.1875$ dollars.