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Ber [7]
4 years ago
6

Frank and Gertrude mow lawns for extra money over the summer. Frank's income is determined by f(x) = 5x + 15, where x is the num

ber of hours. Gertrude's income is g(x) = 4x + 20. If Frank and Gertrude were to combine their efforts, their income would be h(x) = f(x) + g(x). Create the new function h(x). If Frank works 4 hours and Gertrude works 4 hours, and if they each get half of the money when they work together, will Frank make more money working alone or by teaming with Gertrude?
Mathematics
1 answer:
Zepler [3.9K]4 years ago
3 0
H(x)=5x+15+4x+20

if x=4, together it would be 5(4)+15+4(4)+20
h(x)=20+15+16+20=71
Divided by 2, they'd each get 35.5

If Frank worked alone, he'd get 5(4)+15= 35
He'd make more working together. 
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Two certificates of deposit pay interest that differ by 3%. Money invested for one year in the first CD earns $240 interest. The
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a = interest rate of first CD

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and again, let's say the principal invested in each is $X.

\bf a-b=3\qquad \implies \qquad \boxed{b}=3+a~\hfill \begin{cases} \left( \frac{a}{100} \right)X=240\\\\ \left( \frac{b}{100} \right)X=360 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{a}{100} \right)X=240\implies X=\cfrac{240}{~~\frac{a}{100}~~}\implies X=\cfrac{24000}{a} \\\\\\ \left( \cfrac{b}{100} \right)X=360\implies X=\cfrac{360}{~~\frac{b}{100}~~}\implies X=\cfrac{36000}{b} \\\\[-0.35em] ~\dotfill\\\\

\bf X=X\qquad thus\qquad \implies \cfrac{24000}{a}=\cfrac{36000}{b}\implies \cfrac{24000}{a}=\cfrac{36000}{\boxed{3+a}} \\\\\\ (3+a)24000=36000a\implies \cfrac{3+a}{a}=\cfrac{36000}{24000}\implies \cfrac{3-a}{a}=\cfrac{3}{2} \\\\\\ 6-2a=3a\implies 6=5a\implies \cfrac{6}{5}=a\implies 1\frac{1}{5}=a\implies \blacktriangleright 1.2 = x\blacktriangleleft

\bf \stackrel{\textit{since we know that}}{b=3+a}\implies b=3+\cfrac{6}{5}\implies b=\cfrac{21}{5}\implies b=4\frac{1}{5}\implies \blacktriangleright b=4.2 \blacktriangleleft

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