If Auggie is 2 years older than 6 times Elin's age. The sum of their ages is less than 44. What is the oldest Elin could be? Show all your work.

Question

Its inequalities i need help really bad

Answer 1

First, represent Elin as x because Auggie's age in the problem is based off of Elin's age. Since Auggie's age is six times Elin's plus two, their age would be represented as 6x + 2.

Auggie = 6x + 2

Elin = x

Then, the combination of their two ages is less than 44. This means this problem is an inequality.

6x + 2 + x < 44

Combine like terms

7x + 2 < 44

Isolate x by subtracting by 2

7x < 42

Divide by 7 to get x by itself

x < 6

The oldest Elin could be is less than 6 years old, because the sum of their ages cannot be exactly 44, it must be less than.

Answer 2

Let A = Auggie's current age

Let E = Elin's current age

A is 2 more than 6 times Elin's age

A = 2 + 6E

The sum of their ages is less than 44.

A+E < 44

But we have an expression for A in terms of E:

2 + 6E + E < 44

7E + 2 < 44

7E < 42

E < 6

Elin must be less than 6 years old.

When Elin is 5, Auggie is 2 + 30 and 5 + 32 is less than 44.

But is Elin is 6, Auggie is 2 + 36 and 6 + 38 equals 44 (not less than).