5th grade word problem

[Liam]

There are 5 times as many red peppers as green peppers. There are 32 more red peppers than green peppers. How many peppers are there altogether?

I figured out the answer (48) by trial and error, but I don't know how to get it using a method. Can you show me?

 

[Mrspi]

There are 5 times as many red peppers as green peppers. There are 32 more red peppers than green peppers. How many peppers are there altogether?

I figured out the answer (48) by trial and error, but I don't know how to get it using a method. Can you show me?

I think at the fifth grade level, the "guess and check" (another name for "trial and error") method is expected.

But, you can certainly solve this problem using algebra.

Let g = number of green peppers
Let r = number of red peppers

Since we know that there are 5 times as many red peppers as green peppers,
r = 5g

And we also know that there are 32 more red peppers than green peppers:
r = g + 32

You've got two expressions, each of which is equal to r. Those expressions must be equal to each other:

5g = g + 32

Solve that for g, use the result to determine r, and then realize that the question asks for the total number of peppers, which is r + g.

 

[Loren]

There are 5 times as many red peppers as green peppers. There are 32 more red peppers than green peppers. How many peppers are there altogether?

I figured out the answer (48) by trial and error, but I don't know how to get it using a method. Can you show me?

5 times greens = reds
greens + 32 = reds.

Since reds = 5 X greens, substitute that into the second equation, getting...

1 X greens + 32 = 5 X greens.

Therefore 32 = 5 X greens minus 1 X greens.

32 = 4 X greens

If 4 greens = 32, then one greens = 8.

But, 5 X greens = reds.

So 5 X 8 = reds.

reds = 40.
greens = 8.

Check. Are there 5 times as many reds as greens? 5 X 8 - 40. Yes.
Are there 32 more reds than greens? 8 + 32 = 40. Yes.

 

[Liam]

Thank you to mrsp and Loren. When would you start to do it this way? In 6th grade?