Chapter MPS, Problem 3.2MPS

(a)

To determine

To Find: Equation that represents the given situation

Answer to Problem 3.2MPS

  $\begin{array}{l}\text{⇒}13x+4y=\$487\left(\text{equation }1\right)\\ \text{⇒}6x+2y=\$232\left(\text{equation }2\right)\end{array}$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Number of bushes in first order}=13\\ \text{Number of tree in first order}=4\\ \text{Total amount paid by school in first order}=\$487\\ \text{Number of bushes in second order}=6\\ \text{Number of tree in second order}=2\\ \text{Total amount paid by school in second order}=\$232\end{array}$

Formula Used:

  $\text{→}\text{number of bushes}\left(\text{cost of one bushe}\right)+\text{Number of tree}\left(\text{cost of one tree}\right)=\text{Total amount paid by school}$

Calculation:

  $\begin{array}{l}\text{Let the cost of one bushes}=x\\ \text{Let the cost of one tree}=y\\ \text{→}\text{number of bushes}\left(\text{cost of one bushe}\right)+\text{Number of tree}\left(\text{cost of one tree}\right)=\text{Total amount paid by school}\\ \text{⇒}13x+4y=\$487\left(\text{equation }1\right)\\ \text{⇒}6x+2y=\$232\left(\text{equation }2\right)\end{array}$

Conclusion:

(b)

To determine

To Find:The price of one bushe and one tree.

Answer to Problem 3.2MPS

  $\begin{array}{l}\text{cost of one bushes}=\$23\\ \text{cost of one tree}=\$47\end{array}$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Number of bushes in first order}=13\\ \text{Number of tree in first order}=4\\ \text{Total amount paid by school in first order}=\$487\\ \text{Number of bushes in second order}=6\\ \text{Number of tree in second order}=2\\ \text{Total amount paid by school in second order}=\$232\end{array}$

Formula Used:

  $\text{→}\text{number of bushes}\left(\text{cost of one bushe}\right)+\text{Number of tree}\left(\text{cost of one tree}\right)=\text{Total amount paid by school}$

Calculation:

  $\begin{array}{l}\text{→}\text{number of bushes}\left(\text{cost of one bushe}\right)+\text{Number of tree}\left(\text{cost of one tree}\right)=\text{Total amount paid by school}\\ \text{⇒}13x+4y=\$487\left(\text{equation i}\right)\\ \text{⇒}6x+2y=\$232\left(\text{equation ii}\right)\\ \text{⇒}13x+4y=\$487\\ \text{⇒}\left(6x+2y=\$232\right)\times 2\left(\text{multiply equation ii by }2\right)\\ \text{⇒}13x+4y=\$487\left(\text{equation iii}\right)\\ \text{⇒}12x+4y=\$464\left(\text{equation iv}\right)\\ \text{⇒}x=\$23\\ \text{⇒}13\left(\$23\right)+4y=\$487\left(\text{using the value of }x\text{ in equation iii to get }y\right)\\ \text{⇒}\$299+4y-\$299=\$487-\$299\left(\text{subtract both side by }\$299\right)\\ \text{⇒}4y=\$188\\ \text{⇒}y=\$47\end{array}$

Conclusion:

Thus the cost of one bushe and tree is $\$23,\$47$