f) Dailin is mowing lawns at $\$ 40$ per hour to save for a new bike which is $\$ 670$ . He can save $65 \%$ of his lawn mowing money and his dad will give him $\$ 3$ for every $\$ 2$ he can save. $\newline$ How many hours will he need to mow lawns to save enough money for his bilke?

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Q. f) Dailin is mowing lawns at

\$ 40

per hour to save for a new bike which is

\$ 670

. He can save

65 \%

of his lawn mowing money and his dad will give him

\$ 3

for every

\$ 2

he can save.

\newline

How many hours will he need to mow lawns to save enough money for his bilke?

Define Variables: Let's define the variables: $\newline$ - Let $x$ be the number of hours Dailin needs to mow lawns. $\newline$ - Dailin earns $\$40$ per hour, so his total earnings will be $\$40x$ . $\newline$ - He can save $65\%$ of his earnings, so his savings from mowing will be $\$40x \times 0.65$ . $\newline$ - His dad will give him $\$3$ for every $\$2$ he saves. This means for every $\$2$ Dailin saves, he gets an additional $\$3$ from his dad, making it a total of $\$5$ for every $\$2$ saved. $\newline$ - The cost of the new bike is $\$40$ $1$ . $\newline$ We need to find the value of $x$ that will allow Dailin to save enough money to buy the bike.
Calculate Savings from Earnings: Calculate the amount Dailin saves from his earnings: $\newline$ Savings from earnings = $65\%$ of total earnings $\newline$ Savings from earnings = $0.65 \times (\$)40x$ $\newline$ Savings from earnings = $(\$)26x$
Calculate Additional Amount from Dad: Calculate the additional amount Dailin's dad will give him based on his savings: $\newline$ For every $\$2$ saved, Dailin gets $\$3$ from his dad. $\newline$ So, for $\$26$ saved (which is $13$ times $\$2$ ), Dailin will get $13$ times $\$3$ from his dad. $\newline$ Additional amount from dad = $13 \times \$3$ $\newline$ Additional amount from dad = $\$39$ x
Calculate Total Amount: Calculate the total amount Dailin will have after saving and receiving money from his dad: $\newline$ Total amount = Savings from earnings + Additional amount from dad $\newline$ Total amount = $\$26x + \$39x$ $\newline$ Total amount = $\$65x$
Set Up Equation: Set up the equation to find out how many hours Dailin needs to work to afford the bike: $\newline$ Total amount needed for the bike = $\$670$ $\newline$ $\$65x = \$670$
Solve for x: Solve for x to find out how many hours Dailin needs to mow lawns: $\newline$ $\$65x = \$670$ $\newline$ $x = \$670 / \$65$ $\newline$ $x = 10.3076923077$ $\newline$ Since Dailin cannot work a fraction of an hour, we'll round up to the nearest whole hour. $\newline$ $x = 11$ hours