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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 \$ 200 at first.\newlineHe 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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Full solution

Q. Luke had $200 \$ 200 at first.\newlineHe 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?
  1. Understand the problem: Understand the problem.\newlineLuke initially had $200\$200. He spent four times as much in the evening as he did during the day and ended up with $5\$5.\newlineWe need to find out how much he spent during the day.
  2. Denote amounts: Let's denote the amount Luke spent during the day as DD. Then, the amount he spent in the evening is four times that, which is 4D4D.
  3. 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\$200 - D - 4D = \$5
  4. Combine terms: Combine like terms and solve for DD.
    $200−D−4D=$5\$200 - D - 4D = \$5
    $200−5D=$5\$200 - 5D = \$5
  5. Isolate variable: Subtract $200\$200 from both sides to isolate the variable term.\newline−5D=$5−$200-5D = \$5 - \$200\newline−5D=−$195-5D = -\$195
  6. Solve for D: Divide both sides by −5-5 to solve for D.\newlineD=−$(195)/−5D = -\$(195) / -5\newlineD=$(39)D = \$(39)

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