Given
First : They assembled 20 regular wreaths and 16 deluxe wreaths, which used a total of 140 pinecones
Let's represent regular wreaths with r
and
Let's represent deluxe wreaths with d
[tex]20r+16d=140[/tex]Second: They assembled 20 regular wreaths and 18 deluxe wreaths, using a total of 150 pinecones
[tex]20r+18d=150[/tex]We now have
[tex]\begin{gathered} 20r+16d=140\text{ ...Equation 1} \\ 20r+18d=150\text{ ...Equation 2} \end{gathered}[/tex]we can now solve simultaneously, by subtracting the equation 1 and 2
[tex]\begin{gathered} 20r-20r+16d-18d=140-150 \\ -2d=-10 \\ Divide\text{ both sides by -2} \\ -\frac{2d}{-2}=-\frac{10}{-2} \\ \\ d=5 \end{gathered}[/tex]We can subsitute d=5 in equation 1 or 2
[tex]\begin{gathered} 20r+16d=140\text{ ... Equation 1} \\ 20r+16(5)=140 \\ 20r+80=140 \\ 20r=140-80 \\ 20r=60 \\ divide\text{ both sides by 20} \\ \frac{20r}{20}=\frac{60}{20} \\ \\ r=3 \end{gathered}[/tex]The final answer
5 pinecones on the deluxe wreath and 3 pinecones on the regular wreath
