Question

Jon is 3 years younger than Laura. The product of their ages is 1,330. If j represents Jon's age and j + 3 represents Laura's age, what value of j
could be Jon's age?

Answer 1

Answer:

35

Step-by-step explanation:

j(j + 3) = 1330

Trial and error method:

j and j + 3 are pretty close to each other. Start by taking the square root of 1330.

sqrt(1330) = 36.5. One number is less than 36.5 and the other number if 3 more than that.

Since the product of j and j + 3 is 1330 which ends in 0, it is a multiply of 10 and 5.

Try 35 and 38. 35 * 38 = 1330

Answer: 35

Equation method:

j(j + 3) = 1330

j^2 + 3j - 1330 = 0

(j + 38)(j - 35) = 0

j = -38 or j = 35

Answer: 35

Answer 2

If Jon is 3 years younger than Laura, then Jon's age is 35years.

Let the age of John be j

If Jon is 3 years younger than Laura, then;

Laura's age = j + 3

Based on the question, we are told that the product of their ages is 1,330, this can be expressed as:

j(j+3) = 1330

Expand

j²+3j = 1330

j²+3j - 1330 = 0

j²+38j-35j-1330 =0

j(j+38)-35(j+38) = 0

(j−35)(j+38) = 0

j = 35 and j = -38

j = 35

Hence Jon's age is 35years.

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