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Question

# Citywide Ministries plans a five-day ski trip for children. The children may ski from one to five of the days, but the number scheduled to ski each day is the following:$\begin{matrix} \text{Day} & \text{No. of Skiers}\\ \text{Monday} & \text{15}\\ \text{Tuesday} & \text{22}\\ \text{Wednesday} & \text{19}\\ \text{Thursday} & \text{24}\\ \text{Friday} & \text{31}\\ \end{matrix}$Citywide Ministries can obtain two-day lift tickets for $36 each or three-day lift tickets for$47. Find the number of tickets they should purchase for each two-day period and each three-day period so that each child can ski on the day scheduled and that minimizes the cost of lift tickets.

Solution

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Step 1
1 of 5

Firstly we are going to set the substitution. We are going to determine the possible ways to buy a lift ticket for two days or three days in the span of five days. Since there are $4$ ways to buy a two-day lift ticket and $3$ ways to buy a three-day lift ticket, we are going to label those ways as $x_1$, $x_2$, $x_3$, $x_4$, $x_5$, $x_6$, and $x_7$ where $x_1$, $x_2$, $x_3$, and $x_4$ represent the lift tickets bought for first and second, second and third, third and fourth, and fourth and fifth day respectively, and $x_5$, $x_6$, and $x_7$ represent the projectors bought in a first, second and third, a second, third, and fourth, and a third, fourth, and fifth day respectively.

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