AUMENTOS Y DESCUENTOS SUCESIVOS PORCENTUALES METODO GRAFICO Y ANALITICO

Summary

This video tutorial explains how to solve percentage-based problems involving successive increases and discounts. The first example involves calculating a worker’s new salary after successive increases of 20% and 10%. The second example demonstrates how to calculate the final price of a TV after three successive discounts: 20%, 10%, and 5%. The video shows two methods for solving each problem: a graphical method and a mathematical approach. The calculations are explained step-by-step to make the concepts easy to understand, with the final answers clearly provided.

Takeaways

• 😀 The problem involves calculating the new salary after two successive percentage increases: 20% for outstanding performance and 10% for a union claim.
• 😀 In the graphical method, the original salary is divided into 10 equal parts, each representing 10% of the salary.
• 😀 The 20% increase is calculated by multiplying 180 by 2, giving 360. This is added to the original salary of 1800, resulting in 2160.
• 😀 The second increase of 10% is calculated by dividing the new salary of 2160 into 10 parts, each worth 216, then adding 216 to the new salary to get the final salary of 2376.
• 😀 The same problem can be solved using percentage multipliers, where the original salary of 1800 is first multiplied by 120% (1.2), resulting in 2160, then by 110% (1.1), resulting in 2376.
• 😀 The second part of the script describes a problem involving successive discounts on a TV purchase.
• 😀 The original price of the TV is 2400 soles. A 20% discount is applied for the first discount, calculated by dividing 2400 by 10 (240), and multiplying by 2 to get 480. The new price after the first discount is 1920.
• 😀 The second discount of 10% is applied to the new price (1920). By dividing 1920 by 10 (192), the 10% discount is calculated as 192, resulting in a new price of 1728.
• 😀 The third discount of 5% is applied to the price after the second discount (1728). Dividing 1728 by 10 gives 172.8, and half of this is 86.4, which is subtracted from 1728, giving a final price of 1640.16 soles.
• 😀 The same problem can also be solved by multiplying successive percentage multipliers: 80% (after 20% discount), 90% (after 10% discount), and 95% (after 5% discount), resulting in a final price of 1640.16 soles.
• 😀 Both methods for solving the problems give consistent results, reinforcing the importance of understanding percentage increases and decreases in practical financial contexts.

Q & A

What is the first method used to solve the salary increment problem in the transcript?

The first method used is a graphical method, where the initial salary of 1800 soles is divided into 10 parts, each representing 10% of the total amount.

How is the 20% salary increase calculated for José in the first method?

The 20% increase is calculated by dividing the initial salary of 1800 soles into 10 parts (each part equals 180 soles). Then, the 20% increment is the sum of two parts (180 + 180), which equals 360 soles.

What is José’s new salary after the 20% increase?

José’s new salary after the 20% increase is 2160 soles, which is the result of adding 360 soles to his original salary of 1800 soles.

How is the second increment (10%) calculated in the salary problem?

The second increment is calculated by dividing José's new salary of 2160 soles into 10 parts, with each part representing 10% of the new amount. Each part is 216 soles, and the 10% increment is 216 soles.

What is José’s final salary after the second increment?

José’s final salary, after the second increment of 10%, is 2376 soles, which is the result of adding 216 soles to his salary of 2160 soles.

What method is used to calculate the price of the TV in the second problem (discounts)?

The second problem is solved using a graphical method as well. The original price of the TV (2400 soles) is divided into 10 parts, each representing 10% of the total price.

How is the first discount of 20% on the TV calculated?

The 20% discount is calculated by dividing the original price of the TV (2400 soles) into 10 parts, each representing 240 soles. Then, the 20% discount is 480 soles (240 + 240), and the new price after the first discount is 1920 soles.

What is the price of the TV after the second discount of 10%?

After the second 10% discount, the price of the TV is calculated by dividing 1920 soles into 10 parts (192 soles each), and the 10% discount is 192 soles. The new price after this discount is 1728 soles.

How is the third discount (5%) on the TV calculated?

The third discount is calculated by dividing 1728 soles into 10 parts, with each part representing 172.8 soles. The 5% discount is half of 10%, which is 86.4 soles. The final price of the TV after this discount is 1640.16 soles.

What is the alternative method used to calculate the final price of the TV?

The alternative method calculates the final price by applying each discount sequentially to the original price. After a 20% discount, 80% of the original price is paid, followed by a 10% discount (90% of the new price), and finally, a 5% discount (95% of the new price). The final price is 1640.16 soles.