A boy is 7 years older than his brother . In 2 years he will be twice as old as his brother . Find the present ge for eac

Question

i need help on my math problems for my homework 

Answer 1

I believe the question was supposed to ask, "Find the present age for each."

 

If so, try first writing the information given into equations. Try using "a" for the "age of the boy" and "b" for the "age of the brother," where the units for "a" and "b" are in years.

 

Equations:

 

1) "boy is 7 years older than his brother":

 

a = b + 7

(read as: "The boy is the brother's age plus 7 years.")

 

2) "In 2 years, he ("the boy") will be twice as old as his brother":

 

a = (b + 2)(2)

(Read as: "The boy's age is the brother's current age plus 2 years. Then, doubled, or multiplied by 2.")

 

*Note: The brothers age in two years is multiplied by 2, because the boy's age is going to be twice the brother's age in two years. In other words, you're doubling the brother's "new age," where the "new age"= (current brother's age + 2 years) = (b + 2).

 

Now, re-arrange one of the equations to solve for the same variable. Let's start by solving for variable "a" first. The first equation is already simplified and set to solve for "a", therefore only the second equation needs to be simplified and arranged, so that it also solves for "a":

a = (b + 2)(2)

a = 2b + 4 (This is our new equation format that is now set up to solve for "a".)

 

Now that both equations are simplified and set to solve for the same variable, the two equations can be set to equal each other; making only one variable remain. In this case, the variable that remains to be solved for in the equations is "b":

b + 7= a = 2b + 4

 

Re-written as:

b + 7 = 2b + 4

 

Solve by first moving the variables to one side, then use the order of operations to solve for "b." This is the brothers age in years ("yrs").

 

b + 7 = 2b + 4

    - b = - b

      7 = 2b + 4 - 1b (Continue to solve for "b")

 

Now that you have solved for "b", you can plug the "b" value/answer into one of the first two equations, to find the boy's age "a", in years ("yrs"). Either of the first two equations should give you the same value for "a", so pick whichever one you want to use first. To double check your work, use the other equation to solve for "a", using the same "b" value/answer, and see if both values/answers for "a" are the same. If so, you have correctly solved the boy's age "a".

 

*Note: remember to report your answers for both the boy's age and the brother's age in the correct units.

 

Answer 2

Let x = the age of the younger brother

Let x + 7 = the age of the older brother

(x + 7) + 2 = 2(x + 2)

x + 9 = 2x + 4

5 years = x

x + 7 = 12 years