Question

1) Thomas' height increased by 5% from last year to this year. Write two equivalent equations to represent the relationship between Thomas' height, h, last year and his height, t, this year. 2) This year, he is 5 feet and 3 inches tall. How tall was Thomas last year? Bee sure to include units in your answer. Show your work.

Answer 1

1) To represent the relationship between Thomas' height, h, last year and his height, t, this year, we can write two equivalent equations:

Equation 1: t = h + 0.05h

In this equation, we add 5% of Thomas' height last year (0.05h) to his height last year (h) to get his height this year (t).

Equation 2: t = 1.05h

In this equation, we multiply Thomas' height last year (h) by 1.05, which represents an increase of 5%, to get his height this year (t).

2) This year, Thomas is 5 feet and 3 inches tall. To find out how tall he was last year, we need to convert his height this year to a consistent unit.

Let's convert his height to inches:

Height this year = 5 feet + 3 inches = 5 * 12 + 3 = 63 inches

Now, let's use Equation 2 to find Thomas' height last year

t = 1.05h

63 = 1.05h

Divide both sides of the equation by 1.05:

h = 63 / 1.05

h ≈ 60 inches

Therefore, Thomas was approximately 60 inches tall last year.