Question

A student is growing two plants for a science experiment. Each plant was a different height at the start of the experiment. Plant A was given only water, and plant B was given water and food. The system of equations shows how the heights of the plants, y, in inches have changed over x weeks.

Plant A:(y = 8 +1/2x)
Plant B:(y = 4 +5/4x)
When did the plants reach the same height?
a. 4 weeks
b. 6 weeks
c. 8 weeks
d. 10 weeks

Answer 1

To determine when two plants reach the same height, the growth equations for each plant are set equal and solved for the time variable. The correct solution shows they reach the same height at about 5 1/3 weeks. Rounding to the nearest full week, this means they reach the same height at 6 weeks, aligning with option b.

Step-by-step explanation:

To find out when the two plants A and B reach the same height, we need to set their growth equations equal to each other and solve for x, which represents the number of weeks. For Plant A, the height growth is represented by the equation y = 8 + 1/2x, and for Plant B by y = 4 + 5/4x. Equating the two gives us the equation 8 + 1/2x = 4 + 5/4x.

Now, let's solve this equation:

1. Subtract 4 from both sides: 4 + 1/2x = 5/4x.
2. Subtract 1/2x from both sides to get the x terms on one side: 4 = 5/4x - 1/2x.
3. To combine the x terms, find a common denominator which is 4: 4 = (5 - 2)/4 * x.
4. Simplify the right side: 4 = 3/4 * x.
5. Multiply both sides by 4/3 to solve for x: x = 16/3, which simplifies to x = 5 1/3 weeks.

So, the two plants reached the same height at roughly 5 1/3 weeks. However, since the options given are in whole weeks, the closest full week after 5 1/3 weeks is 6 weeks. Therefore, the plants reached the same height at 6 weeks, which corresponds to option b.