How do I solve this?

Question

Pea plants usually produce 5 or 6 peas in each pod. Suppose a pea plant had 5 pods and a total of 26 peas. How many of its pods would have only 5 peas? How many of its pods would have 6 peas? How many peas could a pea plant have if it had 6 pods?

Answer 1

I would recommend drawing a picture to answer the first and second question. The problem tells us that there are 5 pods, so I would draw 5 circles. Each circle represents a pea pod. Next, the problem tells us that there is a total of 26 peas. We could draw dots in each circle to represent peas, so one dot equals one pea. We could place the first dot in the first circle, the second dot in the second circle and so on until we have 26 peas. Following this, we could count the number of dots in each circle. We would find that 4 pods have 5 peas, or 4 circles with 5 dots, and that 1 pod has 6 peas, or 1 circle with 6 dots.

For the third question about 6 pods, we know that each pod has 5 to 6 peas. We could set up a two simple multiplication problems...

6x5 (6 pods with 5 peas in each pod)

6x6 (6 pods with 6 peas in each pod)

We could use skip counting to solve these problems, or we could draw another picture like the one above to determine who many peas 6 pods could make.

Answer 2

Assuming that there are ONLY 5 or 6 in a pod, you could create a table like this that shows all the possibilities and the sum of each.

This shows that the only combination that adds to 26 is 4 fives and 1 six.

But a better way is to use algebra.

Let f be the number of "five-pea" pods and "s" be the number of "six-pea" pods.

f + s = 5 (because there are 5 pods

The total number of peas will be 5f + 6s and that total must be 26. That gives us two equations:

f + s = 5

5f + 6s = 26

Using the first equation, we could subtract "s" from both sides to get:

f = 5 - s

Then, using the second equation, we could replace "f" with "5 - s" wherever there is an "f" like this:

5f + 6s = 26

5(5 - s) + 6s = 26 [then distribute the 5 to get:

25 - 5s + 6s = 26 [then combine like terms to get:

25 + s = 26 [then subtract 25 from both sides to get:

s = 1

Using the modified first equation (f = 5 - s) we can plug in s = 1 like this:

f = 5 - s

f = 5 - 1

f = 4

So there are 4 five-pea pods and 1 six-pea pods.

Remember this ONLY works if you assume that all pods have either 5 or 6 peas.