My son is 7 times older than my grandson and i am 12 times older than my grandson .if you added all of our ages together the sum is 100 years. can you tell me my age in years

Let us suppose my grandson age is x years.

Given my son is 7 times older my grandson so my grand son age =7x.

My age is 12 times older my grandson age so my age = 12x

Sum of all the ages is given as 100 years

We can form an equation with this information

x+7x+12x=100

Adding all the like terms

20x=100

Dividing both sides by 20

x=5

The question is asking to find my age.

My age=12x=12(5)=60

My age is 60 years.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions