Question 1170623: What is the answer to A shipment from a toy factory has a total of 65 unicycles, bicycles, and skateboards combined. The shipment had 160 total wheels. The number of bicycles wheels was the same as the number of skateboard wheels. Create and solve a system of equations to find how many each type of toy was in the shipment. Also I need to show my work.
Found 4 solutions by ikleyn, Boreal, Theo, akumpo:
Answer by ikleyn(52914)   (Show Source):
You can put this solution on YOUR website! .
Hello, I read these words "Also I need to show my work."
and I do not understand what they mean.
Would you say "Also I need to show YOUR work as if it is my work"
- - - then I do understand the exact meaning.
But will not work for you - D E F I N I T E L Y.
Choose the words CAREFULLY to express your thoughts in an ADEQUATE form.
Answer by Boreal(15235)  (Show Source):
You can put this solution on YOUR website! U+2B+4S=160
2B=4S so B=2S
U+B+S=65
2nd into first and third
U+2B+2B=160
U+1.5B=65, multiply above by -1 and add
-U-4B=-160
-2.5B=-95
B=38 bicycles and 76 wheels
S=19 skateboards and 76 wheels
U=8
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! u = number of unicycles
b = number of bicycles
s = number of skateboards.
u + b + s = 65
the shipment had a total of 160 wheels.
the number of bicycle wheels was the same as the number of skateboard wheels.
the number of wheels per unicycle = 1.
the number of wheels per bicycle = 2
the number of wheels per skateboard = 4
the equation for this is:
u + 2 * b + 4 * s = 160
you are given that the number of bicycle wheels was the same as the number of skateboard wheels.
the equation for this is:
2 * b = 4 * s
you have 3 equations that needs to be solved simultaneously.
they are:
u + b + s = 65
u + 2 * b + 4 * s = 160
2 * b = 4 * s
in the equation of 2 * b = 4 * s, solve for b to get:
b = 2 * s
replace b with 2 * s in the other 2 equations to get:
u + 2 * s + s = 65
u + 2 * (2 * s) + 4 * s = 160
combine like terms to get:
u + 3 * s = 65
u + 8 * s = 160
subtract the first equation from the second to get:
5 * s = 95
solve for s to get:
s = 19
since b = 2 * s, then b = 38
in the equation of u + b + s = 65, replace b with 38 and s with 19 to get:
u + 38 + 19 = 65
solve for u to get:
u = 65 - 38 - 19 = 8
your solution is:
number of unicycles = 8
number of bicycles = 38
number of skateboards = 19
confirm your solution by replacing u and b and s with those numbers in both original equations to get:
u + b + s = 65 becomes 8 + 38 + 19 = 65 which becomes 65 = 65, confirming the first equation is true with those numbers.
u + 2b + 4s = 160 becomes 8 + 76 + 76 = 160 which becomes 160 = 160, confirming the second equation is true with those number.
in addition, the number of wheels on the bicycles is equal to the number of wheels on the skateboards which was one of the pieces of given information in the problem.
consequently, the solution is confirmed to be good.
Answer by akumpo(8)  (Show Source):
You can put this solution on YOUR website! let u be the number of unicycles, b the number of bicycles, and s the number of skateboards
u+b+s=65
u+2b+4s=160, b and s are multiplied because of the wheels, since bicycles have two wheels, we multiply the number of bicycles by 2 to get the number of wheels for the bicycles, same with skateboards
Also, if the bicycle wheels equal the skateboard wheels, there are twice as many bicycles as skateboards, as 2 bicycles have the same amount of wheels as 1 skateboard.
So, 2s=b
u+b+s also equals u+2s+s, since 2s=b
u+2b+4s also equals u+4s+4s, since 2b would equal 4s
u+3s=65
u+8s=160
Subtract to get rid of the u variable
-5s=-95
Divide by -5 to get s=19
If there are 19 skateboards, then there are 38 bicycles, because there are twice as many bicycles as skateboards. Also there are 65 total vehicles, so subtract 38 and 19 from 65 to get 8.
CHECK:
u+b+s=65
8+38+19=65
TRUE
u+2b+4s=160
8+(2*38)+(4*19)=160
8+76+76=160
TRUE
There are 8 unicycles, 38 bicycles, and 19 skateboards.
The equations used are:
u+b+s=65
u+2b+4s=160
2s=b
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