Question

A local florist charges $8 for a red rose and $10 for a white rose. He sold twice as many red roses as white roses for a total income of $8,554 for the day. How many roses did he sell all together?

Answer 1

r = amount of red roses w = amount of white roses

"He sold twice as many red roses as white roses" that means, r = twice "w" or "2w"
"or a total income of $8,554" so he sold many "r" and "w" and he ended up making $8,554

well, we know that "r" cost $8 each
we also know that "w" cost $10 each

so however amount he sold of "r", he sold "8r" dollars of red roses
and however amount he sold of "w", he sold "10w" dollars of white roses

we know that they amount to $8,554

so we could say that \(\bf 8{\color{red}{ r}}+10w=8,554\qquad but\qquad {\color{red}{ r}}=2w\qquad thus \\ \quad \\

8{\color{red}{ r}}+10w=8,554\implies 8({\color{red}{ 2w}})+10w=8,554
\)

solve for "w" to see how many white roses she sold

how many red roses did she sell? well, r= 2w, that means that whatever amount of white roses she sold, red roses were twice as much