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Luke had
$200 at first.
He spent four times as much in the evening as in the day. He had $5 left.
How much did Luke spend in the day?

Luke had $\$ 200$ at first. $\newline$ He spent four times as much in the evening as in the day. He had \$\(5\) left.\(\newline\)How much did Luke spend in the day?

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Add and subtract money amounts: word problems

Full solution

Q. Luke had

\$ 200

at first.

\newline

He spent four times as much in the evening as in the day. He had \$\(5\) left.\(\newline\)How much did Luke spend in the day?

Understand the problem: Understand the problem. $\newline$ Luke initially had $\$200$ . He spent four times as much in the evening as he did during the day and ended up with $\$5$ . $\newline$ We need to find out how much he spent during the day.
Denote amounts: Let's denote the amount Luke spent during the day as $D$ . Then, the amount he spent in the evening is four times that, which is $4D$ .
Set up equation: Set up the equation based on the information given. Luke's initial amount - amount spent in the day - amount spent in the evening = amount left $\newline$ $\$200 - D - 4D = \$5$
Combine terms: Combine like terms and solve for $D$ .
$\$200 - D - 4D = \$5$
$\$200 - 5D = \$5$
Isolate variable: Subtract $\$200$ from both sides to isolate the variable term. $\newline$ $-5D = \$5 - \$200$ $\newline$ $-5D = -\$195$
Solve for D: Divide both sides by $-5$ to solve for D. $\newline$ $D = -\$(195) / -5$ $\newline$ $D = \$(39)$

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