In PTA fundraising activity, couples who came were charged $400. However if only one parent came, he was charged $250.00.

59 People attended the activity and $12,150 was raised. How many couples attended?

Mashirio
Nov 22, 2015

#3**+5 **

A CHALLENGE TO YOU

I have just been playing around with a harder version of this question.

Say you have all that info EXCEPT you do not know how many people attended.

In PTA fundraising activity, couples who came were charged $400. However if only one parent came, he was charged $250.00.

59 People attended the activity and $12,150 was raised. How many couples attended?

You want to know all the possibilities of how many singles and how many couples attended.

I mean all the possible pairs of numbers in order for EXACTLY $12,150 to be raised.

Can you do that ?

I found exactly 6 posibilities. Can you find ANY or all of those?

GOOD LUCK :))

Melody
Nov 22, 2015

#1**+5 **

There can be two equations with two variables: C = number of couples; S = number of singles.

One equation is for the number of people: 2C + S = 59

(59 is the total number of people, use '2C' because each couple contains two persons.)

The other equation holds the amount of money made: 400C + 250S = 12,150

Combining these two equations:

Keep the money equations : 400C + 250S = 12,150

Mutiply the number of people equation by 200: 400C + 200S = 11,800

Subtract down the columns: 50S = 350

Divide by 50: S = 7 (there were 7 single parents)

Since 2C + S = 59 ---> 2C + 7 = 59 ---> C = 26 (there were 26 couples)

geno3141
Nov 22, 2015

#2**+5 **

In PTA fundraising activity, couples who came were charged $400. However if only one parent came, he was charged $250.00.

59 People attended the activity and $12,150 was raised. How many couples attended?

Let C=number of couples

Let S=number of singles

2C + S=59,and,

400C + 250S=12,150

Solve the following system:

{2 C+S = 59 | (equation 1)

400 C+250 S = 12150 | (equation 2)

Swap equation 1 with equation 2:

{400 C+250 S = 12150 | (equation 1)

2 C+S = 59 | (equation 2)

Subtract 1/200 × (equation 1) from equation 2:

{400 C+250 S = 12150 | (equation 1)

0 C-S/4 = (-7)/4 | (equation 2)

Divide equation 1 by 50:

{8 C+5 S = 243 | (equation 1)

0 C-S/4 = -7/4 | (equation 2)

Multiply equation 2 by -4:

{8 C+5 S = 243 | (equation 1)

0 C+S = 7 | (equation 2)

Subtract 5 × (equation 2) from equation 1:

{8 C+0 S = 208 | (equation 1)

0 C+S = 7 | (equation 2)

Divide equation 1 by 8:

{C+0 S = 26 | (equation 1)

0 C+S = 7 | (equation 2)

Collect results:

**Answer: | C=26 and S=7**

Guest Nov 22, 2015

#3**+5 **

Best AnswerIn PTA fundraising activity, couples who came were charged $400. However if only one parent came, he was charged $250.00.

A CHALLENGE TO YOU

I have just been playing around with a harder version of this question.

Say you have all that info EXCEPT you do not know how many people attended.

59 People attended the activity and $12,150 was raised. How many couples attended?

You want to know all the possibilities of how many singles and how many couples attended.

I mean all the possible pairs of numbers in order for EXACTLY $12,150 to be raised.

Can you do that ?

I found exactly 6 posibilities. Can you find ANY or all of those?

GOOD LUCK :))

Melody
Nov 22, 2015