Question

1. e a t ea = 15 at = 9 find et 2. b i g ig = 15 bg = 40 find bi 4. f o r fo = 3y + 4 or = 20 fr = 5y + 18 find y 5. f u n fu = 6x un = 5x + 18 fn = 15x - 2 find x find fo find fn

Explanation:

Step1: Find ET in the first part

Since $ET=EA + AT$, and $EA = 15$, $AT=9$, then $ET=15 + 9=24$.

Step2: Find BI in the second part

We know that $BG=BI + IG$. So $BI=BG - IG$. Given $IG = 15$ and $BG = 40$, then $BI=40-15 = 25$.

Step3: Find y in the fourth part

Since $FR=FO + OR$, we substitute the given expressions: $5y + 18=(3y + 4)+20$.
Simplify the right - hand side: $5y+18=3y + 24$.
Subtract $3y$ from both sides: $5y-3y+18=3y-3y + 24$, which gives $2y+18=24$.
Subtract 18 from both sides: $2y+18 - 18=24 - 18$, so $2y=6$.
Divide both sides by 2: $y = 3$.

Step4: Find FO when $y = 3$

Substitute $y = 3$ into the expression for $FO$: $FO=3y + 4=3\times3+4=9 + 4=13$.

Step5: Find x in the fifth part

Since $FN=FU + UN$, we substitute the given expressions: $15x-2=6x+(5x + 18)$.
Simplify the right - hand side: $15x-2=11x + 18$.
Subtract $11x$ from both sides: $15x-11x-2=11x-11x + 18$, which gives $4x-2=18$.
Add 2 to both sides: $4x-2 + 2=18 + 2$, so $4x=20$.
Divide both sides by 4: $x = 5$.

Step6: Find FN when $x = 5$

Substitute $x = 5$ into the expression for $FN$: $FN=15x-2=15\times5-2=75 - 2=73$.

Answer:

1. $ET = 24$
2. $BI = 25$
3. $y = 3$, $FO = 13$
4. $x = 5$, $FN = 73$