Question

mulch to cover a rectangular garden costs 48. mulch is needed to cover a larger, similar garden. the ratio of dimensions is 2:3. how much would it cost to cover the larger

Answer 1

$\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------$

$\bf \cfrac{\stackrel{small}{garden}}{\stackrel{large}{garden}}\qquad \stackrel{sides~ratio}{\cfrac{2}{3}}\qquad \stackrel{\textit{area ratio}}{\cfrac{s^2}{s^2}}\implies \cfrac{2^2}{3^2} \\\\\\ \cfrac{2^2}{3^2}=\cfrac{\stackrel{small~area~cost}{48}}{\stackrel{large~area~cost}{a}}\implies \cfrac{4}{9}=\cfrac{48}{a}\implies a=\cfrac{9\cdot 48}{4}$

the ratio of the cost, is tandem to the ratio of the areas, because, to get the cost for the mulch, you have to first know how many square meters/feet have, and then you apply the cost evenly, now, the cost is just a factor, therefore, the ratio is retained.

Answer 2

Answer: $108

Step-by-step explanation: