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. $\newline$ How many weeks will pass before Kiera and Mitchell have the same amount of money? How much money will they each have? $\newline$ In _ weeks, Kiera and Mitchell will each have $\$$ _.

Full solution

Q. 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.

\newline

How many weeks will pass before Kiera and Mitchell have the same amount of money? How much money will they each have?

\newline

In ___ weeks, Kiera and Mitchell will each have

\$

___.

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.