The cost to rent a condo at a ski resort in Lake Tahoe for a weekend is equally shared by 8 friends. If 3 more people could join them and share the cost, the cost per person would decrease by \$30. What is the total cost to rent the condo for the weekend?

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Hi,

8 people(\$x dollars per person) = 11 people(#x - 30 dollars per person)

8x = 11(x - 30)

8x = 11x - 330

3x = 330

x = 110

Originally each of 8 people were going to pay \$110 each, so the total cost to rent the condo is \$880. <==ANSWER

I hope that helps!! :-)

• If 8 people save \$30 each that's a total savings of \$240. So the following equation will be true: 8x + 240 = 11x where x is the cost per person. When you solve the equation that gives you that x = 80 per person when there is 11 people so the total trip will cost \$880.

To see that's true, if the cost is \$880 split among the original 8 people, that is a cost of \$110 each. When three more people join, each person saves \$30 dropping the cost per person to \$80 each for the eleven. Hope that helps.

• at the same time Alan, Betty, and Chris have \$31. A+B+C = 31: Eqn a million locate the quantity each has if Betty has \$3 below Alan, B = A-3 : Eqn 2 and Chris has \$a million better than Alan and Betty mixed. C = A + B + a million : Eqn3 placed eqn 2 into eqn a million and into eqn 3 A + A -3 + C = 31 2 A + C = 34 : eqn 4 C = A + A-3+ a million 2 A - C = 2 : Eqn 5 upload eqn 4 & eqn 5 4 A = 36 A = 9 B = A -3 = 9 -3 = 6 A+B+C = 31 9+6 +C = 31 15+ C = 31 C = sixteen

• at the same time Alan, Betty, and Chris have \$31. A+B+C = 31: Eqn a million locate the quantity each and each has if Betty has \$3 below Alan, B = A-3 : Eqn 2 and Chris has \$a million better than Alan and Betty mixed. C = A + B + a million : Eqn3 positioned eqn 2 into eqn a million and into eqn 3 A + A -3 + C = 31 2 A + C = 34 : eqn 4 C = A + A-3+ a million 2 A - C = 2 : Eqn 5 upload eqn 4 & eqn 5 4 A = 36 A = 9 B = A -3 = 9 -3 = 6 A+B+C = 31 9+6 +C = 31 15+ C = 31 C = sixteen

• C/8 – C/11 = 30

11C – 8C = 30(8)(11)

3C = 2640

C = 2640/3 = \$880 cost to rend the condo for the weekend

• Let x = the total cost to rent the condo.

Then, x/8 = the average cost for the 8 friends.

And, x/11 = the average cost for 11 people.

x/11 = x/8 - 30

Multiply everything by 88 to clear the fractions to get:

8x = 11x - 2640

Subtract 11x from both sides to get

-3x = -2640

Divide both sides by -3 to get:

x = 880

Hope this helps!! =)