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Hunter and Eva each opened a savings account on the same day. Hunter started by putting $200\$200 in his account, and he will deposit an additional $150\$150 each week. Eva made an initial deposit of $600\$600, and she will add $50\$50 more each week. Eventually, Hunter and Eva will each have the same amount saved. How many weeks will that take?\newlineWrite a system of equations, graph them, and type the solution.\newline____\_\_\_\_ weeks\newline

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Q. Hunter and Eva each opened a savings account on the same day. Hunter started by putting $200\$200 in his account, and he will deposit an additional $150\$150 each week. Eva made an initial deposit of $600\$600, and she will add $50\$50 more each week. Eventually, Hunter and Eva will each have the same amount saved. How many weeks will that take?\newlineWrite a system of equations, graph them, and type the solution.\newline____\_\_\_\_ weeks\newline
  1. Define Variables: Let's define x as the number of weeks, and y as the total amount saved. For Hunter, the equation based on his savings pattern is:\newliney=150x+200 y = 150x + 200
  2. Hunter's Equation: For Eva, her savings equation is:\newliney=50x+600 y = 50x + 600
  3. Eva's Equation: To find when they will have the same amount saved, set the equations equal to each other:\newline150x+200=50x+600 150x + 200 = 50x + 600
  4. Set Equations Equal: Simplify the equation by subtracting 5050x and 200200 from both sides:\newline150x+200−50x−200=50x+600−50x−200 150x + 200 - 50x - 200 = 50x + 600 - 50x - 200 \newline100x=400 100x = 400
  5. Simplify Equation: Solve for x by dividing both sides by 100100:\newlinex=400100 x = \frac{400}{100} \newlinex=4 x = 4

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