What is the ratio value shown by this double number line?

Mathematics

1 answer:

OlgaM077 [116]3 years ago

5 0

The answer is 21/6

Explanation: the next number in the pattern would be 21 since this is linear

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$\bf \begin{cases} a\\\\ b \end{cases}\qquad \qquad \begin{array}{llll} \stackrel{\textit{the sum of \underline{a} and \underline{b}}}{a+b=33}\\\\ \stackrel{\textit{the sum of 7 times \underline{a} and 5 times \underline{b}}}{7a+5b=197} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ a+b=33\implies \boxed{b}=33-a \\\\\\ \stackrel{\textit{substituting \boxed{b} in the second equation}}{7a+5\left(\boxed{33-a} \right)=197}\implies 7a+165-5a=197$

$\bf 2a+165=197\implies 2a=32\implies a=\cfrac{32}{2}\implies \blacktriangleright a=16 \blacktriangleleft \\\\\\ \boxed{b}=33-a\implies b=33-16\implies \blacktriangleright 17\blacktriangleleft$