![\bold{\huge{\green{\underline{Solution }}}}](https://img.qammunity.org/2023/formulas/mathematics/middle-school/4diirzixny4qh46ft8tpsoo0l438ct0yrr.png)
![\bold{\underline{ Given :-}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/t1mlwm6inwlw2q1ccxjjuw5pss6p7kxne5.png)
- We have given that , The cooking time for a leg of lamb is 2/5 hours for each pound
![\bold{\underline{ To \: Find :-}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/fbp4wx5hkpcnwpr19kdfudjhyjlsjf772g.png)
- We have to find , how long should we cook a leg of lamb that weighs 12 3/4 pounds .
- How many hours before we have to cook the food so that it will be ready on time for dinner ?
![\bold{\underline{ Let's \: Begin :-}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/5h1hzzpy32z5mfm1x4raruig2ri2ilboka.png)
Answer (a) :-
According to the question,
![\sf{( 2)/(5)}{\sf{ \:hours = 1 \:pound }}](https://img.qammunity.org/2023/formulas/mathematics/middle-school/7pznez6tknryf3phcl16o1ekh8r5ue8ook.png)
Therefore,
![\sf{ For \: 12}{\sf{( 3)/(4)}}{\sf{\: hours}}](https://img.qammunity.org/2023/formulas/mathematics/middle-school/ngywpblxfii1yzjhy393tsssr4gsz6fzi3.png)
![\sf{ = }{\sf{( 51)/(4)}}{\sf{ × }}{\sf{(2)/(5)}}](https://img.qammunity.org/2023/formulas/mathematics/middle-school/wt6ss4ddarebfno27kjqopk1p4dno6hhj2.png)
![\sf{ = }{\sf{( 102)/(20)}}](https://img.qammunity.org/2023/formulas/mathematics/middle-school/cf878mtayyrgeq6edmd1oeoj4g54fhbjpv.png)
![\sf{ = 5.1 \: hours }](https://img.qammunity.org/2023/formulas/mathematics/middle-school/rquspokgk8zlv7q628x75luxqvvpr33hbp.png)
![\sf{\red{ = 5\: hours\: 6\: minute }}](https://img.qammunity.org/2023/formulas/mathematics/middle-school/hla95ed76y97gon8dgcxagyh6mkzt3iil7.png)
Hence, To cook a leg of lamb weighs 51/4 pounds requires 5 hours 6 minutes
Answer ( b) :-
We have to start cooking before atleast 5.2 hours so that food is ready on the Time for dinner.
- 5.2 hours because serving and dressing of food also take some time.