El agente ordenó otros 625 lápices a precio reducido, y al final, el gastó la misma cantidad por todos los lápices.
¿Cuántos lápices compró y cuál fue el precio de los primeros 300 lápices?
A purchasing agent was going to spend $153 on pencils, but he managed to negotiate a price reduction of
2 1/2 ¢ for each pencil after the first 300 were purchased.
The agent then ordered an additional 625 pencils at the reduced price, and ended up spending the same amount for all of the pencils.
How many pencils did he purchase, and what was the price of the first 300 pencils?
The agent then ordered an additional 625 pencils at the reduced price, and ended up spending the same amount for all of the pencils.
How many pencils did he purchase, and what was the price of the first 300 pencils?
| 1) 10 centavos cada uno | 3) 91/2 centavos cada uno |
| 2) 9 centavos cada uno | 4) 81/2 centavos cada uno |
| 1) 10 ¢ each | 3) 91/2 ¢ each |
| 2) 9 ¢ each | 4) 81/2 ¢ each |
Incorrect. Try again.
Excellente!
Solución:
Deje que
La fórmula cuadrática nos da la solución de esta ecuación
Porque p > 0, usamos
Solución:
Deje que
p = precio original de cada uno de los lápices, en centavos
x = numero original de lápices
El primer trato:
x = numero original de lápices
p*x=15300 --- (1)
El trato nuevo:
p = precio de cada uno de los primeros 300 lápices
p - 2.5 = precio de el resto de los lápices
(x – 300) + 625 = el número de otros lápices comprados
p - 2.5 = precio de el resto de los lápices
(x – 300) + 625 = el número de otros lápices comprados
(p*300) + (p – 2.5)(x+325) = 153000 --- (2)
Al solver por x el resultado es
x = 250p – 325 --- (3)
Si substituimos el resultado (3) en la ecuación (1) por x, obtenemos
p = 179/20 = 81/2 cada uno
Excellent!
Solution:
Let
Quadratic formula solves the last equation and gives
Since p > 0, we take
Solution:
Let
p = original price of each pencil in cent
x = original number of pencils
Old deal:
x = original number of pencils
p*x=15300 --- (1)
New deal:
p = price of each of first 300 pencils
p - 2.5 = price of the rest of the pencils
(x – 300) + 625 = the number of other pencils bought
p - 2.5 = price of the rest of the pencils
(x – 300) + 625 = the number of other pencils bought
(p*300) + (p – 2.5)(x+325) = 153000 --- (2)
Solving for x yields
x = 250p – 325 --- (3)
Substituting the result (3) into equation (1) for x, we have
p = 179/20 = 81/2 cent each