Kiera and her brother, Mitchell, are saving money to adopt a puppy. Kiera currently has 126 $ and plans to save an additional 14 $ each week. Mitchell currently has 42 $ and plans to save an additional 20 $ each week. How many weeks will pass before Kiera and Mitchell have the same amount of money? How much money will they each have? In ____ weeks, Kiera and Mitchell will each have $____.

Question

Kiera and her brother, Mitchell, are saving money to adopt a puppy. Kiera currently has 126 $ and plans to save an additional 14 $ each week. Mitchell currently has 42 $ and plans to save an additional 20 $ each week. How many weeks will pass before Kiera and Mitchell have the same amount of money? How much money will they each have?    In ____ weeks, Kiera and Mitchell will each have $____.

Bytelearn · Accepted Answer

Set up equations:  Let's set up equations for Kiera and Mitchell's savings over time. Kiera's total money after $ w $ weeks is $ 126 + 14w $ dollars. Mitchell's total money after $ w $ weeks is $ 42 + 20w $ dollars. Find equal amount:  Set the equations equal to find when they have the same amount: $ 126 + 14w = 42 + 20w $. Solve for w:  Solve for $ w $: Subtract $ 14w $ from both sides to get $ 126 = 42 + 6w $. Subtract 42:  Subtract 42 from both sides: $ 84 = 6w $. Divide by 6:  Divide both sides by 6 to find $ w $: $ w = 14 $. Calculate final amounts:  Calculate how much money each will have in 14 weeks. For Kiera: $ 126 + 14 \times 14 = 320 $ dollars. For Mitchell: $ 42 + 20 \times 14 = 322 $ dollars.

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