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The number 94 is divided so that 1/5 th of the first part and 1/8 th of the second are in the ratio 3 : 4. what is the first part?

User JakeDK
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Final answer:

To find the first part of the number 94 divided into two parts with a given ratio, we set up two equations with the first part as x and the second part as y, and solve for x to get the value 65.

Step-by-step explanation:

Finding the First Part of the Divided Number

The student is presented with a problem where the number 94 is divided into two parts. The given condition is that 1/5th of the first part and 1/8th of the second part are in the ratio 3:4. To solve this, we need to set up a proportion to find the values of the two parts. Let's denote the first part as x and the second part as y.

According to the given ratio, we have:

  1. 1/5 of the first part (x) is to 1/8 of the second part (y) as 3:4.
  2. Therefore, (1/5)x / (1/8)y = 3/4
  3. By cross-multiplying, we get: 8*(1/5)x = 3*(1/8)y
  4. Which simplifies to: 8x = 15y

We also know that x + y = 94 since the two parts together make the number 94. Now, we have a system of equations:

  1. x + y = 94 (Equation 1)
  2. 8x = 15y (Equation 2)

Solving these equations simultaneously gives us the values of x and y. From Equation 2, we get y = (8/15)x. Substituting this into Equation 1 gives x + (8/15)x = 94, which simplifies to (23/15)x = 94. Solving for x, we get x = (15/23)*94, which equals to 65. So, the first part is 65.

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