Question

# A toy company manufactures bicycles, tricycles, and cars. It is known that 945 wheels will be needed to manufacture 280 toys in total and in addition, it was determined that 10 fewer bicycles will be manufactured than tricycles. Determine the number of toys of each type that you will make.

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## Answer to a math question A toy company manufactures bicycles, tricycles, and cars. It is known that 945 wheels will be needed to manufacture 280 toys in total and in addition, it was determined that 10 fewer bicycles will be manufactured than tricycles. Determine the number of toys of each type that you will make.

Hank
4.8
Definamos las variables:

x = \text{número de bicicletas}
y = \text{número de triciclos}
z = \text{número de autitos}

Sabemos que:

1. Se producirán 10 bicicletas menos que triciclos:
x = y - 10

2. La cantidad total de juguetes es 280:
x + y + z = 280

3. El número total de ruedas es 945:
2x + 3y + 4z = 945

Sustituyendo x = y - 10 en las otras ecuaciones:

$y - 10$ + y + z = 280
2$y - 10$ + 3y + 4z = 945

Resolviendo primero para z :

2y - 20 + 3y + 4z = 945
5y + 4z - 20 = 945
5y + 4z = 965

De la primera ecuación:

2y + z = 290

Multiplicamos la primera ecuación por 2 para alinear los términos:

4y + 2z = 580

Restamos esta ecuación de la ecuación modificada anterior:

$5y + 4z$ - $4y + 2z$ = 965 - 580
y + 2z = 385
y = 385 - 2z

Sustituyendo y en la ecuación 2y + z = 290 :

2$385 - 2z$ + z = 290
770 - 4z + z = 290
770 - 3z = 290
3z = 480
z = 160

Sustituyendo z de nuevo para encontrar y :

y = 385 - 2$160$
y = 385 - 320
y = 65

Y finalmente x :

x = y - 10
x = 65 - 10
x = 55

Por lo tanto, el número de juguetes de cada tipo es:

x = 55
y = 65
z = 160

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