Let u = # of unicycles, t = # of tandem, b = # bikes, r = tricycles.

I started with the wheels. Since there are 32 bikes, 64 of the 115 wheels must have come from bikes. The other ones came from the unicycles, tandems, and tricycles. Unicycles have 1 wheel, tandems have 2 and tricycles have 3.

115 – 64 = u + 2t + 3r and the number of unicycles= number of tandem so

51 = u +2u + 3r

51 = 3u +3r

There are 57 helmets total, so there must be 57 seats. A unicycle, bike, and tricycle all have one seat and a tandem has 2 seats. Since there are 32 bikes, you know that 32 of the 57 helmets are from the bikes.

57 – 32 = u + 2t + r and t = u

25 = u + 2u + r

25 = 3u + r

So r= 25-3u. Plug this into the equation we got for wheels:

51= 3u+3r

51= 3u +3(25-3u)

51 = 3u + 75 -9u

51-75= – 6u

-24 = -6u

u = 4 so t = 4

and you know that 25 = 3u + r

so 25 = 12 +r and r= 13.

Check it and it works

also you start with u=tm bikes do trial and error 4,5,6,7

32 reg bikes = 64 wheels 32 helmets

4 unicycles = 4 wheels 4 helmets

4 tandem = 8 wheels 8 helmets

______ ____

Subtotal 76 44

115-76=39 57-44=13

13 tricycles 39 wheels 13 helmets

Thats your answer.

So glad to help.

1. There are four variables, unicycles (u), tandems (t), regular bikes (b), and trikes (k).

2. u = t

3. b = 32

4. u + t + b + k = 57

5. 1u + 2t + 2b + 3k = 115

So we fill everything in:

u + t + b + k = 57

u + u + 32 + k = 57

2u + k = 25

k = 25 – 2u

1u + 2t + 2b + 3k = 115

1u + 2u + 2(32) + 3k = 115

3u + 3k = 115 – 64

3u + 3k = 51

3(u + k) = 3(17)

u + k = 17

Now combining the two results:

u + k = 17

u + (25 – 2u) = 17

-u = 17 – 25

-u = -8

u = 8

8 unicycles

8 tandems

u + k = 17

8 + k = 17

k = 9

9 trikes

32 bikes

Done!

think——

57 bikes- 32 bikes=25 bikes left to figure out

115-64= 51 the amount of wheels left to figure out

(32 regular bikes) X (2 wheels each)= 64

a tandem bike has 2 wheels & unicycles have 1 wheel & tricycles have 3……….

y= # of tricycle

x= # of unicycles and tandems (since it has to be the same #)

115= 64+3y+1x+2x

-64 -64

51= 3y+1x+2x

divide 51 and 3y by 3 to cancel out y in order to find x (its hard to do it on computer) you get……….

17= 1x+2x

-1 -1 to cancel out 1 x in order to find 2x

16=2x divide 16 and 2x by 2

your answer 16/2=8

x=8

now plug 8 into your problem to get y

115= 64+3y+1(8)+2(8)

115= 64+3y+8+16 simplify your problem

115= 64+3y+24 simplify your problem

115=88+3y simplify your problem

-88 -88 subtract 88

27=3y divide by 3

y=9

you get 9 tricycles, 8 unicycles & 8 tandems

check your problem

57(amount of bikes/helmets)= 32 reg+9 tri+8 uni+ 9 tan

does this equal?

10 unicycles

10 tandem

5 tricycles