Question

Maggie's brother is 3 years younger than twice her age the sum of their ages is 24. how old is Maggie?

Answer 1

For this case, the first thing we must do is define variables.

We have then:

x: Maggie's age

y: Age of Maggie's brother

We write the system of equations that models the problem.

We have then:

$y = 2x-3\\x + y = 24$

We solve the system of equations.

For this, we use substitution:

$x + (2x-3) = 24$

From here, we clear the value of x:

$3x - 3 = 24\\3x = 24 + 3\\3x = 27$

$x = \frac{27}{3}\\x = 9$

Answer:

Maggie is 9 years old

Answer 2

Maggie's age is 9

Further Explanation

One variable linear equation is an equation that has a variable and the exponent number is one.

Can be stated in the form:

$\large {\boxed {\bold {ax=b}}$

or

ax + b = c,

where a, b, and c are constants, x is a variable

Whereas the two-variable linear equation is a linear equation that has 2 variables and the exponent is one

Can be stated in the form:

$\large {\boxed {\bold {ax + bx = c}}}$

x, y = variable

Let Maggie's age = x

Maggie's brother = y,

In the statement of the task:

• Maggie's brother is 3 years younger than twice her age

we translate this sentence into the equation

y = 2x-3 ... equation 1

• The sum of their ages is 24

we translate this sentence into the equation

x + y = 24 ...equation 2

Both of these equations are equations that have 2 variables, so the solution can be used in 3 ways:

• 1. graph system

the solution is the intersection point of the two equations / lines.

• 2. substitution

the solution is we change one variable  into another variable form of an equation, then substitutes that variable in another equation

• 3. elimination

the solution is to eliminate one variable from the equation system.

to determine the variable x we ​​eliminate the variable y first , or vice versa.

We use the second method: substitution

we substitute equation 1 into equation 2 :

$\displaystyle x+2x-3=24$

$\displaystyle 3x-3=24$

$\displaystyle 3x=27$

$\displaystyle x=9$

So Maggie's age: $\large{\boxed{\bold{9}}$

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Keywords: variable, equation, substitution, elimination, graph, Maggie's age