Answer:
The Inequality with integer coefficient for the total sales is ![5000+3x\geq 10000](https://tex.z-dn.net/?f=5000%2B3x%5Cgeq%2010000)
Hence Jonathan should make total sales of at least <u>1667</u> to earn at least 100.
Step-by-step explanation:
Given:
Amount paid per week = 50
Addition amount = 3% of Total sales.
Let the Total sales be 'x'.
∴ Additional amount = ![\frac{3}{100}x](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B100%7Dx)
Amount he wants to earn this week
100
We need to write the inequality with integer coefficient for the total sales and also to find the total sales.
Solution:
We cans say that;
Amount paid per week plus Additional amount should be greater than or equal to Amount he wants to earn this week.
framing in equation form we get;
![50+\frac{3}{100}x\geq 100](https://tex.z-dn.net/?f=50%2B%5Cfrac%7B3%7D%7B100%7Dx%5Cgeq%20100)
Now we will make the denominator common using LCM we get;
![\frac{50\times100}{100}+\frac{3}{100}x\geq 100](https://tex.z-dn.net/?f=%5Cfrac%7B50%5Ctimes100%7D%7B100%7D%2B%5Cfrac%7B3%7D%7B100%7Dx%5Cgeq%20100)
![\frac{5000}{100}+\frac{3}{100}x\geq 100](https://tex.z-dn.net/?f=%5Cfrac%7B5000%7D%7B100%7D%2B%5Cfrac%7B3%7D%7B100%7Dx%5Cgeq%20100)
![\frac{5000+3x}{100}\geq 100](https://tex.z-dn.net/?f=%5Cfrac%7B5000%2B3x%7D%7B100%7D%5Cgeq%20100)
Multiplying both side by 100 we get;
![100 \times\frac{5000+3x}{100}\geq 100\times 100\\\\5000+3x\geq 10000](https://tex.z-dn.net/?f=100%20%5Ctimes%5Cfrac%7B5000%2B3x%7D%7B100%7D%5Cgeq%20100%5Ctimes%20100%5C%5C%5C%5C5000%2B3x%5Cgeq%2010000)
Hence The Inequality with integer coefficient for the total sales is ![5000+3x\geq 10000](https://tex.z-dn.net/?f=5000%2B3x%5Cgeq%2010000)
On solving the above equation we get;
Subtracting both side by 5000 we get;
![5000+3x-5000\geq 10000-5000\\\\3x\geq 5000](https://tex.z-dn.net/?f=5000%2B3x-5000%5Cgeq%2010000-5000%5C%5C%5C%5C3x%5Cgeq%205000)
Dividing both side by 3 we get;
![\frac{3x}{3}\geq \frac{5000}{3}\\\\x\geq 1666.67](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B3%7D%5Cgeq%20%5Cfrac%7B5000%7D%7B3%7D%5C%5C%5C%5Cx%5Cgeq%201666.67)
Hence Jonathan should make total sales of at least <u>1667</u> to earn at least 100.