Answer :

TSO
The ratio of Isabella’s money to Shane’s money is 3:11

Isabella has $33.   

We can make a proportion to solve for how much money Shane has.   
A proportion is two ratios that are set equal to each other.  

Let’s call Shane’s money ‘S’   

We get this proportion:   3/11 = 33/x   

If we cross multiply we get:   
(33) * (11) = (3) * (x)   

Simplifying it, we get:
363 = (3) * (x)   

Divide both sides by 3, we get:
x = 121   

However, the question asks how much money they have together. 

Isabella + Shane = Total
33 + 121 = $154   

They have $154 together.
johanrusli

If Isabella has $33, then they both have $154

Further explanation

Let the linear equation : [tex]y = mx + c[/tex]

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

m → gradient of the line

( 0 , c ) → y - intercept

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

[tex]\large {\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

[tex]\large {\boxed{y - y_1 = m ( x - x_1 )} }[/tex]

Let us tackle the problem!

Let :

Isabella's money = y

Shane's money = x

If the ratio of Isabella's money to Shane is 3 : 11 then :

[tex]y : x = 3 : 11[/tex]

[tex]3x = 11y[/tex]

[tex]\large {\boxed {x = \frac{11y}{3} } }[/tex]

Isabella has $33 → y = 33

[tex]x = \frac{11y}{3}[/tex]

[tex]x = \frac{11(33)}{3}[/tex]

[tex]x = 121[/tex]

Shane has $121

Isabella and Shane together will have :

x + y = $121 + $33 = $154

Learn more

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Equation , Line , Variable , Line , Gradient , Point

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