Question

The sum of three numbers is 952. One of the numbers, z, is 40% less than the sum of the other two numbers. What is the value of z?

Answer 1

Answer:

z = 357

Step-by-step explanation:

Let the three numbers be denoted as "x", "y" and "z".

We are given that:

z = 40% less than (x + y)

z = (x + y) - 40% of (x + y)

Now, 40% = 40/100 = 0.4

∴ z = (x + y) - 0.4*(x + y)

∴ z = (1 - 0.4)*(x + y)

∴ z = 0.6*(x + y)          ........(i)

We are also given that sum of all three numbers is 952

∴ x + y + z = 952

∴  x + y + 0.6*(x + y) = 952  ...........Using (i)

∴ x + y + 0.6*x + 0.6*y = 952

∴ 1.6*x + 1.6*y = 952

∴ 1.6*(x + y) = 952

∴ (x + y) = 952/1.6

∴ (x + y) = 595 ............(ii)

Now,

x + y + z = 952

=> 595 + z = 952 ............Using (ii)

=> z = 952 - 595

=> z = 357

Verify:

To verify: 357 is 40% less than 595

40% of 595 = 238

A number that is 238 less than 595 is (595 - 238) = 357   (Verified)

Answer 2

Value of z is 357.

• Sum of three numbers is given as 952.
• One number is given as z.
• Given that z is 40% less than the sum of other two numbers.
• That means z is 60% of the sum of both the other numbers.

z = 0.6(sum of other two numbers)

sum of other two numbers = (10/6)z

• Sum of three numbers is 952.

z + (Sum of other two numbers) = 952

z + (10/6)z = 952

(16/6)z = 952

z = 357