Solve Coin, Growth, Time, and Rate Problems

Solve the following math and logic problems. Show the reasoning and identify any assumption needed to interpret the wording. ### Part 1 — Two coins A person has two coins totaling 55 cents. One of the coins is not a nickel, which is worth 5 cents. What are the two coins? #### What This Part Should Cover - A pair of coin denominations that adds to 55 cents. - The distinction between one coin not being a nickel and neither coin being a nickel. ### Part 2 — Daily doubling A tree doubles in height every day. It is 8 feet tall on day 10. On which day is it 5 feet tall? #### What This Part Should Cover - Heights at the relevant integer-numbered days. - Whether daily doubling alone determines the time at which the height reaches 5 feet between observations. ### Part 3 — Minutes until five Fifty minutes ago, the time's distance from 3 p.m., measured in minutes, was four times the number of minutes from now until 5 p.m. How many minutes remain until 5 p.m.? #### What This Part Should Cover - An equation that places both clock times on the same afternoon's timeline. - A check of the resulting current time and the time 50 minutes earlier. ### Part 4 — Pizza consumption A group of 1.5 people eats 1.5 pizzas in 1.5 days. At the same per-person consumption rate, how many pizzas would 9 people eat in 3 days? #### What This Part Should Cover - Consumption expressed in pizzas per person per day. - Scaling by both the number of people and the number of days. ### Part 5 — Meeting in a corridor Two people start at opposite ends of a corridor at the same time and walk toward each other. Person A starts at office 1 and moves at 5 offices per minute. Person B starts at office 46 and moves at 10 offices per minute. At which office do they meet? #### What This Part Should Cover - The separation between the two starting office positions. - Relative speed, meeting time, and a position check from each end. ### What a Strong Answer Covers - The original quantities and units, with calculations that can be checked against each statement. - Explicit treatment of ambiguous wording, particularly the tree's behavior between daily observations. - The constant-rate and office-spacing interpretations used for the rate problems. ### Follow-up Questions - What extra growth model would let you compute a fractional day for the tree? - Why does counting office labels instead of intervals give the wrong corridor separation?