Video: Using Linear Equations to Solve Problems

One way to cook beef is to roast it in the oven at 375Β°F for 15 minutes per pound plus an additional 30 minutes. A joint of beef takes 1 1/4 hours to roast at 375Β°F. What is the weight of the joint?

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Video Transcript

One way to cook beef is to roast it in the oven at 375 degrees Fahrenheit for 15 minutes per pound plus an additional 30 minutes. A joint of beef takes one and a quarter hours to roast at 375 degrees Fahrenheit. What is the weight of the joint?

We’re told in the question that we need to roast the joint of beef for 15 minutes per pound. This can be written as 15𝑝, where 𝑝 is the weight of the joint in pounds. We also need to roast it for an additional 30 minutes. This means that the total cooking time is 15𝑝 plus 30.

We’re also told that a specific joint of beef takes one and a quarter hours to roast. We know that 60 minutes is equal to one hour. This means that 30 minutes is equal to half an hour. And, 15 minutes is equal to a quarter of an hour. One and a quarter hours is therefore equal to 75 minutes, as 60 plus 15 equals 75. We can therefore write the expression for the cooking time equal to 75. 15𝑝 plus 30 equals 75. As we need to calculate the weight of the joint, we need to solve this equation.

Our first step is to subtract 30 from both sides of the equation. On the left-hand side, the 30s cancel, so we are just left with 15𝑝. 75 minus 30 is equal to 45. So, 15𝑝 equals 45. We can then divide both sides of this equation by 15. 15𝑝 divided by 15 is equal to 𝑝. On the right-hand side, we have 45 divided by 15. You might recognize that 15 divides exactly into 45. The answer is equal to three, as 15 multiplied by three is equal to 45.

If you didn’t notice that, we could simplify the fraction by dividing the numerator and denominator by five. 45 divided by five is equal to nine. And, 15 divided by five equals three. 45 over 15 is the same as nine over three. Once again, dividing nine by three gives us an answer of three. The weight of a joint of beef that takes one and a quarter hours or 75 minutes to roast is three pounds.

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