a Soon the Smiths heard about gold found in a river nearby R

a. Soon the Smiths heard about gold found in a river nearby. Richard decided to make pickaxes and shovels to sell to the miners. But Richard’s daughter Kaley wanted to pan for gold. Richard made a deal with Kaley: “I’ll let you pan for gold for one year. If after a year you make more money prospecting than I do selling pickaxes and shovels, I’ll let you continue panning for gold. But if you make less than I do, you agree to return to the family business, stay at home, and work with us.”
Surprise! On her first day of prospecting, Kaley found a gold nugget worth $150! After 2 months, Kaley had taken in $166 (including the $150), and her father had made only $42. After 5 months, Kaley’s total earnings had reached $190, and her father’s total was $105. If Kaley did not find any more large gold nuggets, do you think Kaley would get to keep panning for gold after a year? HINT! Make equations to figure out who makes more after 12 months!

b. The wagon train that your family is a member of has reached Sutter Creek in California. They decide to settle down in the area. Like Biddy Mason and the Smiths, you are now faced with the decision of how to make a living. Create a mathematical problem about some members of your family who either start a business or go for the gold.

Solution

On her first day, Kaley\'s income = 150 $

After that, Kaley\'s monthly income = 8$

So after 12 months kaley\'s total income = 150 + 12*8 = 246$

Her father\'s monthly income = 21 $

after 12 months , father\'s total income = 12*21 = 252$

Hence Kaley would not get to keep panning for gold . She has to return to her family business.