Answer:
£120
Step-by-step explanation:
Let's denote:
- The amount Maz gets as [tex]\bold{x}[/tex],
- The amount Jake gets as [tex]\bold{y}[/tex],
- The amount Lou gets as [tex]\bold{z}[/tex].
Given:
The total amount they share is £370, so we have the equation:
[tex] \sf x + y + z = 370 \quad \cdots \quad (1)[/tex]
The amount Maz and Jake get is in the ratio 2:3, so:
[tex] \sf \dfrac{x}{y} = \dfrac{2}{3} \quad \cdots \quad (2)[/tex]
The amount Jake and Lou share is in the ratio 5:4, so:
[tex] \sf \dfrac{y}{z} = \dfrac{5}{4} \quad \cdots \quad (3)[/tex]
We can use equations (2) and (3) to express [tex]\bold{x}[/tex] and [tex]\bold{y}[/tex] in terms of [tex]\bold{z}[/tex], and then substitute these expressions into equation (1) to solve for [tex]\bold{z}[/tex].
From equation (2), we have:
[tex] \sf x = \dfrac{2}{3}y \quad \cdots \quad (4)[/tex]
From equation (3), we have:
[tex] \sf y = \dfrac{5}{4}z \quad \cdots \quad (5)[/tex]
Substitute equations (4) and (5) into equation (1):
[tex] \sf \dfrac{2}{3}y + y + z = 370[/tex]
[tex] \sf \dfrac{2}{3}\left(\dfrac{5}{4}z\right) + \dfrac{5}{4}z + z = 370[/tex]
[tex] \sf \dfrac{5}{6}z + \dfrac{5}{4}z + z = 370[/tex]
To add fractions, we need a common denominator, which is 12 in this case:
[tex] \sf \dfrac{ 5 \cdot 2\cdot z + 5 \cdot 3\cdot z + 12\cdot z }{12} = 370[/tex]
[tex] \sf \dfrac{ 10z + 15z + 12z }{12} = 370[/tex]
[tex] \sf \dfrac{37}{12}z = 370[/tex]
Now, solve for [tex]\bold{z}[/tex]:
[tex] \sf z = \dfrac{370 \times 12}{37}[/tex]
[tex] \sf z = \dfrac{4440}{37}[/tex]
[tex] \sf z \approx 120[/tex]
Therefore, Lou gets approximately £120.
