Word problem for 6th grader (not doing algebra yet). I'm mom, have answer key but can't figure out how to set it up to show her.

Question

Mrs. Klein made some tarts. She sold 3/5 of them in the  morning and 1/4 of the remainder in the afternoon . If she sold 200 more in the morning than in the afternoon, how many tarts did she make? 

 

Working on my daughter's 6th grade math with her. Have the answer key, not sure how they got the answer.  The answer is 400 (sold 240 and 40) but can't figure out how they got there, have tried working it backwards. So far we've done fine on all the rest. Can someone walk us through? 

Answer 1

This is a problem using fractions.  You are right to teach that "of" usually means multiply.

 

"Mrs. Klein made some tarts. She sold 3/5 of them in the  morning"    means that 3/5 of them are sold

     it also means that (1 - 3/5) of them are left

               that is  (5/5 - 3/5)

                    or  2/5 of them are left

"... and 1/4 of the remainder in the afternoon"    means

           (1/4) * (2/5)               [you did say "of" means multiply, right?]

           (1*2) / (4*5)

               2/20                   [sold in the afternoon; reduce now or later]

                1/10   sold in the afternoon

 

"sold 200 more in the morning than in the afternoon"     now, this is like algebra,

      'how much more (as a fraction) was sold in the morning??'

             3/5 - 1/10

              6/10 -1/10

                5/10

                 1/2          

              in the morning, she sold (half of the total) more than she did in the afternoon.

              in the morning, she sold      200               more than she did in the afternoon.

 

If "half of the total" is 200, what is the total ??    400

 

How many were sold in the morning?    (3/5)*(400) = 240

How many were left until afternoon?    400 - 240 = 160

How many were sold in the afternoon?  (1/4)*(160) = 40

Checking:  Is 240 really 200 more than 40?   yes

Answer 2

suppose she makes X tarts.Now she sold 3/5 of them in morning that means she sold X*3/5 tarts.

she sold 1/4 of remainder in evening.

remainder tarts=X-(X*3/5)=X*2/5

1/4 of remainder is = (X*2/5) *(1/4)=X/10

She sold X/10 Tarts in evening.

 she sold 200 more tarts in the morning than she did in the afternoon

 

Morning tarts = evening tarts + 200

X*3/5           =  (X/10)          + 200

after solving the above equation u will get

X=2000/5 = 400

Answer 3

The student may not be doing algebra, but we can use algebra to verify if the answer the teacher gave is indeed correct.

 

So, if Mrs. Klein made some tarts, and we don't know how many tarts she made, let's make up a number and call it T, because using letters for numbers is fun.

 

If at first she sold 3/5 of the tarts, that means she sold 0.6*T tarts and was left with 0.4*T tarts.

 

Now, she sold 1/4 of the remainder, which means she was left with (3/4)*(2/5)*T = (6/20)*T = (3/10)*T = 0.3*T, which means she sold 0.4*T - 0.3*T = 0.1*T tarts.

 

To summarize that first part, the total number of tarts she sold in the morning is 0.6*T, and the number she sold in the afternoon is 0.1*T. Now, here's where the algebra comes in!

 

0.6*T = 0.1*T + 200 (because she sold 200 more tarts in the morning than she did in the afternoon)

 

That means that 0.5*T = 200, or in other words she made T = 400 tarts!