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

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20-01-2015
Mathematics

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

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carlosego carlosego · Answer 1 · 2018-07-20T08:40:50-04:00

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:

[tex] y = 2x-3

x + y = 24
[/tex]

We solve the system of equations.

For this, we use substitution:

[tex] x + (2x-3) = 24
[/tex]

From here, we clear the value of x:

[tex] 3x - 3 = 24

3x = 24 + 3

3x = 27
[/tex]

[tex] x = \frac{27}{3}

x = 9
[/tex]

Answer:

Maggie is 9 years old

ardni313 ardni313 · Answer 2 · 2019-10-20T23:50:38-04:00

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:

[tex] \large {\boxed {\bold {ax=b}} [/tex]

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:

[tex] \large {\boxed {\bold {ax + bx = c}}} [/tex]

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 :

[tex]\displaystyle x+2x-3=24[/tex]

[tex]\displaystyle 3x-3=24[/tex]

[tex]\displaystyle 3x=27[/tex]

[tex]\displaystyle x=9[/tex]

So Maggie's age: [tex]\large{\boxed{\bold{9}}[/tex]

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