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?
Answers
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:
Looking at our answers, the left side of the range is either 0 or 8. If z = 0 then x = 50 - 0 = 50, which is greater than 4z +10 = 0 + 10 = 10. This gives options of 4,8 or 10 for the right side of the range. If z = 10 then x = 50 - 10 = 40 which is not larger than 4z +10 = 40 + 10 = 50.