5th grade word problem

Question

Jane, Andre, & Maria pick apples. Andre picks three times as many pounds as Maria. Jane picks two times as many pounds as Andre. The total weight of the apples is 840 pounds. How many pounds of apples does Andre pick?

Answer 1

Hi Angela, 

Step 1: We can solve this problem by translating the problem:

If we let x = the pounds Marie picked, we can find Andre and Jane's contribution:

Since the problem says "Andre picked three times as much as Marie," Let 3x = the pounds Andre picked

Since the problem says "Jane picked twice as much as Andre," we have 2(3x), which is 6x.

So, our Let Statements are:

Let x= the pounds Marie picked

Let 3x = the pounds Andre picked

Let 6x = the pounds Jane picked

Step 2: Create an equation

The problem says, "the total weight of the apples is 840," so we know:

Jane+Andre+Maria=840

6x+3x+x=840 Substitute our Let Statements

10x=840 Solve for x

x=84

∴Andre picked 252 pounds because Andre picked 3(84)=252.

Best,

Star

 

Answer 2

The question gives us three equations:

 

1) A = 3M

2) J = 2A

3) J + A + M = 840

 

We can solve for M by substituting equations 1 and 2 into equation 3.

J + A + M = 840

2A + A + M = 840

2(3M) + 3M + M = 840

6M + 3M + M = 840

10M = 840

M = 84

 

Now go back and insert the M variable into equation 1 to get A.

A = 3M

A = 3(84)

A = 252

 

Now plug that into equation 2 to get J.

J = 2A

J = 2(252)

J = 504

 

Hope this helps, Angela!