More math help!!?

Question

This is supposed to be 5th grade?

Anna's farm picked a total of 310 pumpkins. Anna separated the pumpkins into small and large. She sold the small pumpkins for $3 each and the large ones for $9 each. She sold all of the pumpkins for total sales of $1,950. How many small and large pumpkins did Anna originally pick?

MS Exx: that's great but my daughter needs to solve it

Answer 1

s + l = 310
3s + 9l = 1950

s = -l + 310

3(-l + 310) + 9l = 1950
-3l + 930 + 9l = 1950
6l = 1020
l = 170

s = -170 + 310
s = 140

She had 140 small ones and 170 large ones

Check:

140 + 170 = 310 and 3(140) + 9(170) = 1950
310 = 310 and 420 + 1530 = 1950
1950 = 1950

I hope this helps.

Answer 2

OK

To learn how to do this, think of this a system of 2 linear equations, with 2 unknowns.

First equation
s + l = 310 (small plus large - total pumpkins)
3s + 9l = 1950 ($3 for each small, 9 for each large- total sales when added together is 1950). So far, so good.

s+l = 310
3s + 9l = 1950 ; ok lets multiply the top equation by 3. By doing this you will see that the s will go away - watch)

3s + 3l = 930
3s + 9l = 1950; now subtract and the s goes away

-6l = -1020; divide by -6
l = 170

So 170 large pumpkins were sold. Substitute in the first equation - s + 170 = 310 , s = 140

So 140 small pumpkins were sold.

DO the check!
3(140) + 9(170) = 1950 ??
420 + 1530 = 1950??
1950 = 1950 YES!!

OK - there's a pretty simple explanation of how it's done. This is another method different from others. Using what is call "elimination by addition and subtraction". Ms. Ex's method is also valid - "using substitution".

Hope this helps.

Answer 3

Let the numbers of small and large pumpkins be a and b. Then

a + b = 310
3a + 9b = 1 950

Multiply the 1st equation by 3 and subtract it from the 2nd

3a + 9b = 1 950
-(3a + 3b = 930)

6b = 1 020
b = 170

Now use the 1st equation again.

a = 310 - b = 310 - 170 = 140

So she had 140 small pumpkins and 170 large ones.

Happy Halloween!

Answer 4

5th grade?? This is more like 8th grade.
In one variable (x= small pks) and 310-x= large pks.
Then SUM(costxnumber sold)=total sales
or
3x + 9(310-x) = 1950 etc.....

Answer 5

U will be requiring statements

let the small pimpkins be x
let the big pimpkins be y

Total = x + y
310 = x + y or x + y = 310

small was sold @ 3 and big @9
It was sold for 1950

so 3x + 9y = 1950
*----------------------------------------------------
*method 1
*----------------------------------------------------
3x+9y = 1950
x+ y = 310 Multiplying by 3 we get 3x+3y=930

so
3x +9y = 1950
3x +3y = 930 By subtracting we get
--------------------
6y = 1020 so y = 170

substituting in the 1st equation we get
x+170 = 310
x= 310-170
x= 140
*-----------------------------------------------------------
*Method 2
*-----------------------------------------------------------
x+y =310
x=(310-y)

substituting in second Equation

3x+9y = 1950
3(310-y)+9y =1950
930 -3y + 9y = 1950
930 + 6y = 1950
6y = 1950 -930
6y =1020
y = 170

substituting in the 1st equation we get x = 140