Can someone please help me with this word problem?

Question

Mr. Schwinn was taking inventory at his shop. He sells bicycles and tricycles. He counted 127 wheels and 106 pedals. How many bicycles and tricycles does he have in his store?

Answer 1

Hello Jolie,

Let us say that there are t tricycles
and b bicycles.

Then for every trike there are three wheels so we have 3t wheels and for every bike we have two wheels so we have 2b wheels. Therefore:

3t +2b = 127

Also, for every trike we have two pedals so we have 2t pedals and for every bike we have 2 pedals hence 2b pedals. Ergo

2t + 2b = 106

Now subtract the second equation from the first and we get:

t = 21

So we have 21 trikes.

Putting this back into the second equation gives us:

2(21) + 2b = 106 or 42 +2b = 106 hence 2b = 106 - 42
so 2b = 64 and b = 32..

So we have 32 bikes and 21 trikes.

Checking:

2(21) + 2(32) = 42+64=106

3(21) + 2(32) = 63 + 64 = 127

Hope this helps.

Answer 2

There are 3 steps here:
Let letters be the unknowns,
change the word statements into equations,
and solve them.

Let there be B bicycles and T tricycles.
Then the statement about wheels translates to:
2B + 3T = 127
and the one about pedals...
2B + 2T = 106.

Easiest way to solve these 2 equations in 2 unknowns is to substract the lower from the upper. This leaves
T = 127-106 = 21.
To get B, put the answer for T back in one of the original equations. Use the second:
2B + 2(21) = 106, or 2B + 42 = 106
Then 2B = 106-42 = 64, and B = 32.

Answer 3

you would have 53 bikes & tricycles, of which 29 would be bikes, and 23 would be tricycles.

106/2=53 bikes
29+23 =53 bikes
29*2 wheels = 58 wheels
23 *3 wheels = 69 wheels
58+69 = 127 wheels

Answer 4

If you only need to know how many TOTAL of the bikes and trikes he has, then divide 106 by 2. Both kinds have only two pedals each. That means that 127 wheels is just there to confuse you.

If you need to know how many of EACH, then subtract 106 from 127. That gives you the number of trikes. From above, you know how many total units you have, so subtract the number of trikes from that number to tell you how many bikes you have.

To check yourself, multiply 3 and the number of trikes, and 2 times the number of bikes. The sum will confirm the number of wheels.

Answer 5

ok, you know that he has 106 pedals, and regardless of what kind of bike it is, it has two pedals, so divide it by two

Now you know that he has 53 bikes

think of a bike as x

then a tricycle is (x + 1)

so x + (x+1) = 53

subtract the 1 and

2x = 52

x = 26

so he has 26 bikes

subtract 26 from 53 and you get the number of tricycles

27 tricycles


Hope that helped!

Answer 6

T=# of trikes
B=# of bikes

3T + 2B = 127 // times by 3 and 2 for # of wheels

T + B = 53
T = 53 - B

Substituting:
3(53-B) + 2B = 127
159 - 3B + 2B = 127
159 - B = 127
-B = -32
B = 32


T + B =53
T + 32 = 53
T = 53-32
T = 21

There are 21 Trikes and 32 Bikes

Answer 7

Guess & Check
21 Tricycles
32 Bicycles

Answer 8

Total number = pedals / 2 = 53

127 = 3T + 2B
T+B=53

You should be able to solve that