Question Video: Forming and Solving Two-Step Equations Mathematics • 7th Grade

The age of a man is multiplied by 100 and then the product is added to 65. If the result is 3965, how old is the man?

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Video Transcript

The age of a man is multiplied by 100 and then the product is added to 65. If the result is 3965, how old is the man?

We can begin this question by letting the age of the man be 𝑎 years. We are told that this number is multiplied by 100. This can be written as 100𝑎. The product is then added to 65. So, we have 65 plus 100𝑎 or 100𝑎 plus 65. As the result of this is 3965, we can write the equation 100𝑎 plus 65 is equal to 3965. This equation can now be solved using the balancing method and the inverse operations.

We begin by subtracting 65 from both sides of the equation. On the left-hand side, we are left with 100𝑎. On the right-hand side, we have 3900. Our next step is to divide both sides by 100 as division is the inverse or opposite of multiplication. When dividing by 100, all of our digits move two places to the right, so 𝑎 is equal to 39.

We can, therefore, conclude that the age of the man is 39 years. We can check this answer by substituting it back in to the initial equation. 100 multiplied by 39 plus 65 is equal to 3965. Therefore, our answer is correct.

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