At her bike factory, Eleanor manufactures two-wheel and three-wheel bikes. She has 96 seats and 212 wheels in inventory. She wants to use all the seats and wheels. How many three-wheelers should she manufacture?
if there are x 2-wheelers and y 3-wheelers, just count the wheels and seats:
x+y = 96
2x+3y = 212
2x+3(96-x) = 212
x=76, y=20
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To find out how many three-wheelers Eleanor should manufacture, we can set up a system of equations based on the given information.
Let's assume Eleanor manufactures x three-wheelers.
Each three-wheeler requires 3 wheels and 1 seat, so the total number of wheels used by the three-wheelers would be 3x, and the total number of seats used would be x.
Since Eleanor has a total of 212 wheels and wants to use them all, we can write the first equation:
3x = 212
Similarly, since Eleanor has a total of 96 seats and wants to use them all, we can write the second equation:
x = 96
To solve this system of equations, we can substitute the value of x from the second equation into the first equation:
3 * 96 = 212
Simplifying this equation:
288 = 212
However, this equation is not true, which means there is no solution to this system of equations. Therefore, it is not possible for Eleanor to use all the seats and wheels that she has in inventory to manufacture three-wheelers.