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

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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?

Nov 22, 2015

#3
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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 :))

Nov 22, 2015
edited by Melody  Nov 22, 2015

#1
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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)

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:

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
edited by Melody  Nov 22, 2015
#5
+5

How about: 1, 6, 11, 16, 21, 26 couples, and:

47, 39, 31, 23, 15, 7 singles.

Nov 22, 2015
#6
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That sounds good to me. Who is this mysterious guest ??     LOL

I'm thinking Bertie but then I have been known to be wrong  :D

Nov 23, 2015
edited by Melody  Nov 23, 2015