Question

Rewrite the verbal statement as an equation or inequality.

Tonya and her sister Mallory are growing out their hair to donate it for the Pantene
Project. Tonya's hair is 14 inches long and grows 0.5 inches each month. Mallory's hair is
10 inches long and also grows 0.5 inches each month. Write an inequality that could be
used to determine x, the total number of months the girls can grow their hair out so that
the total length of Mallory's hair is less than or equal to the length of Tonya's hair.

Answer 1

To express the statement as an inequality, we have: Tonya's hair length after x months is 14 + 0.5x inches, and Mallory's is 10 + 0.5x inches. The inequality that ensures Mallory's hair is not longer than Tonya's is 10 + 0.5x ≤ 14 + 0.5x.

Step-by-step explanation:

To rewrite the verbal statement as an inequality, we must first represent the growing lengths of Tonya and Mallory's hair mathematically. Tonya's hair is initially 14 inches long, and it grows at a rate of 0.5 inches each month. So, the length of Tonya's hair after x months would be 14 + 0.5x inches. Similarly, Mallory's hair starts at 10 inches and also grows at a rate of 0.5 inches per month, making the length after x months 10 + 0.5x inches. To ensure Mallory's hair never exceeds the length of Tonya's hair, we set up an inequality where the length of Mallory's hair is less than or equal to the length of Tonya's hair, as follows: 10 + 0.5x ≤ 14 + 0.5x. This inequality will help determine x, the total number of months the girls can grow their hair.