Malcom Davis earnings is an illustration of equations and proportions.
- The equation is:
![\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cfrac%7B1%7D%7B90%7DG%3D%20%5Cfrac%7B1%7D%7B60%7D%28G-%20100000%29%7D)
- The gross income must be $300000, for Dave to earn the same amount with either plan.
- His earning is $3333.33 when the plans are the same.
Let the profit be P, and the gross income be G.
So, we have:
![\mathbf{P= G - 100000}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%3D%20G%20-%20100000%7D)
<u>(a) The equations</u>
For plan A, we have:
<em />
<em> ----1/90 of the company's gross income</em>
For plan B, we have:
<em />
<em> ----1/90 of the company's profit</em>
When both are the same, we have:
![\mathbf{A= B}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%3D%20B%7D)
This gives
![\mathbf{\frac{1}{90}G= \frac{1}{60}P}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cfrac%7B1%7D%7B90%7DG%3D%20%5Cfrac%7B1%7D%7B60%7DP%7D)
Substitute ![\mathbf{P= G - 100000}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%3D%20G%20-%20100000%7D)
![\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cfrac%7B1%7D%7B90%7DG%3D%20%5Cfrac%7B1%7D%7B60%7D%28G-%20100000%29%7D)
Hence, the equation is: ![\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cfrac%7B1%7D%7B90%7DG%3D%20%5Cfrac%7B1%7D%7B60%7D%28G-%20100000%29%7D)
<u>(b) Solve the equation in (a), and intepret</u>
![\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cfrac%7B1%7D%7B90%7DG%3D%20%5Cfrac%7B1%7D%7B60%7D%28G-%20100000%29%7D)
Cross multiply
![\mathbf{60G = 90G - 9000 000}](https://tex.z-dn.net/?f=%5Cmathbf%7B60G%20%3D%2090G%20-%209000%20000%7D)
Collect like terms
![\mathbf{90G - 60G = 9000 000}](https://tex.z-dn.net/?f=%5Cmathbf%7B90G%20-%2060G%20%3D%209000%20000%7D)
![\mathbf{30G = 9000 000}](https://tex.z-dn.net/?f=%5Cmathbf%7B30G%20%3D%209000%20000%7D)
Divide both sides by 30
![\mathbf{G = 3000 00}](https://tex.z-dn.net/?f=%5Cmathbf%7BG%20%3D%203000%2000%7D)
The gross income must be $300000, for Dave to earn the same amount with either plan.
<u>(c) His earnings based on (c)</u>
We have:
![\mathbf{A = \frac{1}{90}G}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%20%3D%20%5Cfrac%7B1%7D%7B90%7DG%7D)
Substitute ![\mathbf{G = 3000 00}](https://tex.z-dn.net/?f=%5Cmathbf%7BG%20%3D%203000%2000%7D)
![\mathbf{A = \frac{1}{90} \times 300000}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%20%3D%20%5Cfrac%7B1%7D%7B90%7D%20%5Ctimes%20300000%7D)
![\mathbf{A = 3333.33}](https://tex.z-dn.net/?f=%5Cmathbf%7BA%20%3D%203333.33%7D)
His earning is $3333.33 when the plans are the same
<u>(d) If the gross income in less than (b)</u>
If the gross income is <em>less than $300,000</em>, then plan A would better for Malcom Davis, because his earnings in plan A would be <em>greater than </em>plan B
Read more about equations at:
brainly.com/question/20893366