2070.22 – Alyssa's Formula

Alyssa has a formula that tells her how much she will earn after xx hours of baby-sitting. Tonight, for example, she will be sitting for 5 hours. Her formula will tell her what she will earn. What is her formula and how much will she earn?

It may help if you know that last night Alyssa sat for 3.5 hours and earned $7.45.

Solution

Suppose Alyssa earns dd dollars after hh hours of sitting. Then her hourly rate is dh\dfrac{d}{h} and her earnings are xdh\dfrac{xd}{h}. Since she earned 7.45 last night for 3.5 hours, her rate is $7.453.5=$2.10\dfrac{\$7.45}{3.5} = \$2.10 per hour.

That means her formula is x×2.1x \times 2.1 and tonight after sitting 5 hours she will earn 5×2.1=10.50.5 \times 2.1 = 10.50.

This may be a pretty low rate compared to what your students earn these days. You might take a poll and have them make a formula that fits their rate, using the example of whatever he/she earned for 3.5 hours as a way of making the actual rate non-obvious at first. You could put somebody's numbers on the board and have students to figure out the rate. Sometimes students simply get some money for an evening depending on what's in the parent's wallet. Thus the rate might change. Something else to explore.