Question

The sum of two positive numbers x and z is 50. If x is greater than 10 more than four times z, which of the following includes the entire range of values for z?

Answer 1

Answer:

• 0 < z < 8 includes the entire range of values for z.

Step-by-step explanation:

Given that:

The sum of two positive numbers x and z is 50.

• i.e., x + z = 50
• or, x = 50 - z _____(i)

x is greater than 10 more than four times z.

• i.e., x > 10 + 4z _____(ii)

To Find:

• Which of the following includes the entire range of values for z?

Comparing eqⁿ(i) and eqⁿ(ii):

⇒ 50 - z > 10 + 4z

⇒ 50 - 10 > 4z + z

⇒ 40 > 5z

⇒ 5z < 40

⇒ z < 40/5

⇒ z < 8

∵ z is a positive number.

Entire range of values for z = 0 < z < 8

Answer 2

Solution:

According to the question, sum of two positive numbers x and z is 50. This says that:

$\longrightarrow\tt{x+z = 50}$

$\longrightarrow\tt{x = 50-z---(1)}$

The question also says that x is greater than 10 more than four times z. This says that:

$\longrightarrow$ x > 10 more than Four times z

$\longrightarrow$ x > 10+4z---(2)

Now, let us substitute the value of x from (1) in (2)

$\longrightarrow$ x > 10+4z

$\longrightarrow$ 50-z > 10+4z

$\longrightarrow$ 50-z > 10+4z

$\longrightarrow$ 50-z-4z > 10

$\longrightarrow$ 50-5z > 10

$\longrightarrow$ -5z > 10-50

$\longrightarrow$ -5z > -40

$\longrightarrow$ -5z > -40

$\longrightarrow$ z > 8