math
posted by zachary stanich on .
Bikes, Trikes and more
At Brittany's Bike shop, she rents all kinds of cycles: unicycles, tandems, regular bikes, and even tricycles. She parks all the cycles in front of her shop with a helmet for each rider strapped to the cycles. This morning Brittany counted 57 Helmets and 115 wheels. She knows she an egual number of unicycles and tandems. She also knows that she has 32 regular bikes. How many unicycles, tandems and trikes does she have?

If we let u=unicycles, b=bicycles, t=tandems, k=trikes,
helmets: u+b+2t+k=57
wheels: u+2b+2t+3k=115
u=t
b=32
so we are left with:
t+32+2t+k=57
t+64+2t+3k=115
3t + k = 25
3t + 3k = 51
2k = 26
k=13
t=4
u=4
b=32