Josiah had 80%as much money as Sanithia at first.They bought a present for their friend and shared the cost of the present equally.in the end, Josiah had 35% of the total amount of money left. If the present cast $238,how money did Santhia have at first?
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Let's understand this money problem step by step. Josiah had 80% as much money as Sanithia initially. They bought a present costing 238 dollars and shared the cost equally. After the purchase, Josiah had 35% of their total remaining money. We need to find Sanithia's initial amount.
Now let's set up our variables. Let S represent Sanithia's initial money and J represent Josiah's initial money. Since Josiah had 80% as much money as Sanithia, we write J equals 0.8 times S. The present costs 238 dollars, and they share the cost equally, so each person pays 119 dollars.
After buying the present, let's calculate how much money each person has left. Josiah has J minus 119 dollars, and Sanithia has S minus 119 dollars. The total money remaining is J plus S minus 238. According to the problem, Josiah has 35% of the total remaining money, so J minus 119 equals 0.35 times the total remaining amount.
Now let's solve the equation step by step. We substitute J equals 0.8S into our equation. This gives us 0.8S minus 119 equals 0.35 times the quantity 1.8S minus 238. Simplifying the right side, we get 0.8S minus 119 equals 0.63S minus 83.3. Moving terms to collect like variables, we have 0.17S equals 35.7. Dividing both sides by 0.17, we find that S equals 210.
Let's verify our answer. Sanithia initially had 210 dollars, and Josiah had 168 dollars, which is 80% of Sanithia's amount. After buying the present, Sanithia has 91 dollars left and Josiah has 49 dollars left. The total remaining money is 140 dollars. We can check that 49 divided by 140 equals 0.35 or 35%, confirming our answer. Therefore, Sanithia had 210 dollars at first.