A group of science teachers went to a resturant.Thhy agreed to split the bill equally. When the bill arrived, two them discovered that they had forgotten there money.The others in the group agreed to make up the difference by paying an extra \$1.30 each. If the total bill was \$78 , how many teachers were in the group?

Relevance

There are 12 teachers in the group.

\$78 / 12 = \$6.50 bill for each teacher.

2 teachers forgot their money = \$13.00

That means 10 have to pay the total bill.

\$78/10 = \$7.80

\$7.80 - \$6.50 = \$1.30

~ Mitch ~

Source(s): AJ has NO IDEA how to solve this problem:
• Simple

here,

n = total number of teachers

x1, x2, x3 .... xn are all equal as the share of every member is equal in \$78

Equations. goes like this:

1. x1 + x2 ..... xn = 78

=> nx = 78 -----i

(as x = sum of all x)

2. x1 + x2 = (n-2) * (1.3)

=> 2x = (n-2) * (1.3) -----ii

now we have two equations and we can solve them by system of linear equations:

i => x = 78 / n

ii => (2 * 78) / n = (n-2) * (1.3)

=> 156 / n = (n-2) * (1.3)

=> 156 / 1.3 = n(n-2)

=> 120 = n^2 - 2n

=> n^2 - 2n - 120 = 0 ----iii

now we have a quadratic equation to solve, we will solve it using method of breaking middle terms

iii => n(n-12) + 10(n-12) = 0

=> (n-12) (n+10) = 0

=> n = 12 , n = -10

Here n = -10 is impossible, which means n = 12.

Total Number of Teachers = 12

• The group consisted of 12 teachers.

The bill was \$78, so splitting that evenly means that each should have paid \$6.50.

Since only 10 had their money (ha! a likely story! <g>), they each had to pay \$7.80 towards the bill.

• Anonymous