Question

"Jack’s age is five years more than three times the age of his younger brother, Jimmy. If the sum of their ages is at most 53, find the greatest age that Jack could be. Write and solve an inequality to answer this question. Don't forget to use years old as a label."

Answer 1

To find the greatest age that Jack could be, set up an inequality using the given information. Solve the inequality to find the maximum age Jimmy could be, then substitute this value back into the original equation to find the greatest age Jack could be.

Step-by-step explanation:

To find the greatest age that Jack could be, we need to set up a mathematical inequality using the given information. Let's assume Jack's age is 'J' and Jimmy's age is 'M'. Based on the information given, we can write the inequality:

J = 3M + 5

The sum of their ages is at most 53, so we can write:

J + M ≤ 53

Substituting the value of J from the first equation into the second equation, we have:

(3M + 5) + M ≤ 53

Combining like terms, we get:

4M + 5 ≤ 53

Subtracting 5 from both sides, we get:

4M ≤ 48

Dividing both sides by 4, we get:

M ≤ 12

Therefore, the maximum age that Jimmy could be is 12. Substituting this value back into the first equation, we find:

J = 3(12) + 5 = 41

So the greatest age that Jack could be is 41 years old.