I need help with a 10th grade math word problem?

Question

Wheels "R" Us sells bicycles, tricycles, and unicycles. They have one more bicycle than unicycle in stock. If there are 60 pedals and 80 wheels, how many bicycles, tricycals, and unicycles are there in stock ????

Answer 1

u = unicycles (1 wheel)
b = bicycles (2 wheels)
t = tricycles (3 wheels)

b = u + 1 (b/c there's one more bicycle than unicycle)

Each -cycle has 2 pedals, so 30 total -cycles
u + b + t = 30
u + (u+1) + t = 30
2u + t = 29 --------------- t = 29 - 2u

80 total wheels, so
1u + 2b + 3t = 80
u + 2(u+1) + 3t = 80
u + t = 26 ----------------- t = 26 - u


set the 2 equations for t equal to each other
29 - 2u = 26 - u
u = 3

unicylces = 3
bicycles = 3 + 1 = 4
tricycles = 30 - 3 - 4 = 23

Answer 2

U=Number of Unicycles, B=Number of Bikes, T = Number of Tricycles. There is one more B than U, so B = U + 1.
There are two pedals on every unit, so 2(U + B + T) = 60 (pedals.)
Substitute for B: 2(U + [U +1] + T) = 4U + 2 + 2T = 60, or
4U + 2T = 58, divide both by 2 :
2U + T = 29 (pedals)
If you multiply the number of wheels on each unit and add them together you get another equality: U + 2B + 3T = 80 (wheels.)
Again substitute for B: U + 2(U + 1) + 3T = 3U + 2 +3T = 80
Reducing we get 3U + 3T = 78 then divide both by 3:
U + T = 26 (wheels)
Realizing that we can subtract an equality from an equality:
(2U + T) - (U + T) = 29 - 26, so, Unicycles = 3
There is one more bike than ther are unicycles so there are 4 bikes
We know 2U +T = 29 (pedals), if U = 3, 6 + T = 29 and T = 23
Just to check, we add 23 + 4 + 3 = 30 x 2 = 60 pedals and
3 + (2x4) + (3 x 23) = 3 + 8 + 69 = 80 wheels, I think.

Answer 3

Bicycles have two wheels. If we use B to indicate how many bicycles, there are 2*B wheels and 2*B pedals on them.
Tricycles have three wheels. If we use T to indicate how many tricycles, there are 3*T wheels and 2*T pedals on them.
Unicycles have one wheel. If we use U to indicate how many unicycles, there are U wheels and 2*U pedals on them.

The total wheels is 2*B + 3*T + U = 80
The total pedals is 2*B + 2*T + 2*U = 60, which means that B+T+U=30, if we divide both sides by 2.

We also know that there is one more B than U, so..
B = U + 1

So...
2*(U+1) + 3*T + U = 80
(U+1) + T +U = 30

(2*U + 2) + 3*T + U = 80
U + 1 + T + U = 30

3*T + 3*U = 78
T + 2*U = 29

T + U = 78 / 3 = 26
T + 2*U = 29
U = 3
T = 29 - 2*3 = 23

B = U + 1 = 4

There are 4 bicycles with 8 wheels and 8 pedals
There are 23 tricycles with 69 wheels and 46 pedals
There are 3 unicycles with 3 wheels and 6 pedals

Answer 4

There are 3 unicycles, 4 bicycles, and 23 tricycles. I basically had to use trial and error. Because each "vehicle" had to have two pedals, I knew that there were 30 total. From there, I chose two consecutive numbers and found the number that totalled the other two to 30. I multiplied to find the wheels on each kind. After coming up with a very small number of wheels, I knew that there had to be more tricycles than anything. By lowering the number of bikes and unis, I ended up with 3, 4, and 23. I hope I could help!

Answer 5

Let b= # of bicycles, t= # of tricycles, u= # of unicycles.
Since bicycles have 2 wheels, tricycles have 3 wheels, and unicycles have 1 wheel, while each have 2 pedals, you can set up these equations.

Pedals: 2b+2t+2u=60
Wheels: 2b+3t+u=80
The second equation becomes u=80-2b-3t. Substitute this into the first equation to get 2b+2t+2(80-2b-3t)=60, or b+t+80-2b-3t=30. This simplifies to -b-2t=-50 or b+2t=50. t<=25 and by the Pedals equation b+t+u=30 or b+u>=5.
Subtracting the Pedals equation from the Wheels equation gives t=u+20<=25, so u<=5. Trying u=5 gives t=25, b=0. Trying u=4 gives t=24, b=2. Trying u=3 gives t=23, b=4. Trying u=2 gives t=22, b=6, Trying u=1 gives t=21, b=8.

Answer 6

each have 2 pedals - so i think 30 in all - unicycles have 1 wheel bikes 2 and tricycles have 3 - but you have to just ignore that to find the answer if you are just wanting the total of whats in stock you take total pedals and divide by 2

Answer 7

B = # of bicyclyes
T = # of tricycles
U = # of unicycles

B = U + 1

Pedals
2(U + 1) + 2T + 2U = 60
2U + 2 + 2T + 2U = 60
4U + 2T = 58

Wheels
2(U + 1) + 3T + 1U = 80
2U + 2 + 3T + 1U = 80
3U + 3T = 78

Multiply the wheels equation by 3 and the pedals equation by 2

12U + 6T = 174
6U + 6T = 156

Subtract

6U = 18
U = 3

Substitute into pedals equation

4U + 2T = 58
4(3) + 2T = 58
12 + 2T = 58
2T = 46
T = 23

B = U + 1
B = 4

Pedals check:
2(4) + 2(23) + 2(3) = 60
8 + 46 + 6 = 60
60 = 60

Wheels check:
2(4) + 3(23) + 1(3) = 80
8 + 69 + 3 = 80
80 = 80

Answer 8

every cycle requires two pedeals so max of 30 cycles
dividing 30 by 3 is 10 (use this as a base number)
saying 10 bikes w/ 2 wheels, 10 trikes w/ 3 wheels, 10 uni's with 1 wheel now complet the math
if the total number of wheels exceedes the 80 adjust the numbers by changing the base number of cycles.
Sorry, I won't give the anwser but I like to help tutor when I can and help you see other ways of looking a a problem

Answer 9

ow. but i figured out the answer. 12 bikes.13 tricycals,and 16 unicycles.I feel sorry for you though.HAPPY TO HELP.

Answer 10

Wow, that hurts my head just thinking about it Good luck.