Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. On the windowsill is a plant that is 19 inches tall. It is growing 2 inches per week. A second plant, which is 20 inches tall, is on the coffee table. It is growing 1 inch per week. Eventually the two plants will be the same height. How tall will the plants be? How many weeks will that take? Each plant will be _____ inches tall after _____ weeks.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  On the windowsill is a plant that is 19 inches tall. It is growing 2 inches per week. A second plant, which is 20 inches tall, is on the coffee table. It is growing 1 inch per week. Eventually the two plants will be the same height. How tall will the plants be? How many weeks will that take?   Each plant will be _____ inches tall after _____ weeks.

Bytelearn · Accepted Answer

Define Variables: Let's define the variables: Let $ x $ be the number of weeks that have passed. Let $ y $ be the height of the plants when they are the same height.  We can write two equations to represent the growth of each plant: For the plant on the windowsill: $ y = 19 + 2x $ (since it starts at 19 inches and grows 2 inches per week) For the plant on the coffee table: $ y = 20 + x $ (since it starts at 20 inches and grows 1 inch per week)  We want to find the value of $ y $ and $ x $ when the plants are the same height, so we set the two equations equal to each other: $ 19 + 2x = 20 + x $Write Growth Equations: Now we solve for $ x $ using the equation we just set up: $ 19 + 2x = 20 + x $ Subtract $ x $ from both sides to get: $ 19 + x = 20 $ Subtract 19 from both sides to isolate $ x $: $ x = 20 - 19 $ $ x = 1 $ So, it will take 1 week for the plants to be the same height.Set Equations Equal: Next, we substitute $ x = 1 $ back into one of the original equations to find $ y $, the height of the plants when they are the same height. We can use either equation, but we'll use the first one: $ y = 19 + 2x $ $ y = 19 + 2(1) $ $ y = 19 + 2 $ $ y = 21 $ So, the plants will be 21 inches tall after 1 week.

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