Please help me :( I’m not that good with math

Mathematics

1 answer:

d1i1m1o1n [39]2 years ago

5 0

Answer:

Step-by-step explanation:

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$\bf \stackrel{\textit{3 lbs of "c"}}{3c}+\stackrel{\textit{5 lbs of "w"}}{5w}~~=~~\stackrel{\textit{costs}}{15} \\\\\\ \stackrel{\textit{12 lbs of "c"}}{12c}+\stackrel{\textit{2 lbs of "w"}}{2w}~~=~~\stackrel{\textit{costs}}{33} \end{cases}\qquad \impliedby \textit{let's use elimination} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llccccccl} 3c+5w=15&\times (-4)\implies &-12c&+&-20w&=&-60\\ 12c+2w=33&&12c&+&2w&=&33\\ \cline{3-7}\\ &&0&&-18w&=&-27 \end{array}$

$\bf -18w=-27\implies w=\cfrac{-27}{-18}\implies \blacktriangleright w=\cfrac{3}{2} \blacktriangleleft \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{3c+5\left(\cfrac{3}{2} \right)=15}\implies 3c+\cfrac{15}{2}=15 \implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( 3c+\cfrac{15}{2} \right)=2(15)} \\\\\\ 6c+15=30\implies 6c=15\implies c=\cfrac{15}{6}\implies \blacktriangleright c=\cfrac{5}{2} \blacktriangleleft$

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