Question

Marcia can make 5 candles in an hour. Kevin can make only 4 candles in an hour, but he already has 7 completed candles. Explain to Marcia how she can use a system of equations to determine when she will have the same number of candles as Kevin. Use complete sentences.

Answer 1

M = marcia's total amount of candles

k = kevin's total amount of candles

h = amount of hours

so in 1hr she makes 5(1), in 2hrs she makes 5(2) and 3 she makes 5(3), in "h" hours she makes 5h.

kevin makes in 1hr 4(1), in 2hrs 4(2) and 3hrs 4(3), in "h" hours 4h.  But kevin already has 7 candles done from the day before, so the 4h is really additional to his 7 candles.

$\bf \begin{cases} m=5h\\\\ k=4h+7 \end{cases}\impliedby \textit{when are they equal?}\qquad \stackrel{m}{5h}~~=~~\stackrel{k}{4h+7}\\\\ -------------------------------\\\\ 5h=4h+7\implies h=7$