Here's another math riddle! Deadline: Sunday, Jan.21 @ 5pm PST.?

Question

Darcy runs a tire store. One week she counted up 35 bills of sale. She knew that all of the customers had either bought 4 new tires or 2 new tires. She had 82 old tires to dispose of in the yard. How many customers bought 2 tires and how many bought 4 tires?
Please help me do this algebraically. I know the numbers are 29( 2new) and 6(4new). Email me with any questions!;)

Answer 1

Hello.

The number of old tires are equal to the number of ones to be disposed in the yard. If we take the number of the person who bought 4 tyres "x" and the number of those who bought 2 tyres "y". Then their sum should be 35 (= the number of bills, for each bill represent a buyer).

then: 1) 4x + 2y = 82 & 2) x + y = 35

1) 4x + 2y = 82 >>> 2x +y = 42 >>> y = 41 - 2x; >> inserting this solution into Eq. 2 gives: x + 42 - 2x = 35>>> x = 41 - 35 = 6>>>

x = 6 and therefore y = 41 - 2 (6) = 41 - 12 = 29>>> y = 29. OK?

Answer 2

Let X= the number of people who bought 2 tires
Let Y= the number of people who bought 4 tires

We know that X + Y = 35

and that X*2 + Y*4 = 82

Now you have two equations and two unkowns. You can solve one for X, subsitute into the other and then find Y. Then use your value for Y in one of the equations to solve for X.

Answer 3

X + Y = 35 (total number of sales)
4X + 2Y = 82 (total number of tires)

Solve by simultaneous equations.
You can substitute X = 35 - Y or Y = 35 - X into second equation,
or multiply first equation by - 2 to get
- 2X - 2Y = - 70
and add to second equation
4X + 2Y = 82
to get
2X = 12 (then divide both sides by 2)
so X = 6
and Y = 29 (since X + Y = 35)

Answer 4

Wow... we have to stick to deadlines now?! I, along with a lot of people, are here for fun. If I wanted the stress and hassle of a deadline I'd be back at work doing overtime...

Answer 5

6(4x) + 29(2x) = 35x