Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Quincy and his mom are planting vegetables in their garden. Quincy has finished planting 1 row of carrots so far and is planting new rows at a rate of 4 rows per hour. His mom has finished 8 rows of tomatoes and will continue planting at 3 rows per hour. Once the pair get to the point where they have finished the same number of rows, they will take a break and decide what to plant next. How long will that take? How many rows will they each have completed? In _______ hours, Quincy and his mom will each have planted _______ rows of vegetables. ​

Answer 1

Explanation:

rc = planted rows of carrots

rt = planted rows of tomatoes

h = number of hours

rc = 4h + 1 (starting with 1 already finished row there will be 4 additional rows every hour)

rt = 3h + 8 (staying with 8 already finished rows there will be 3 additional rows every hour).

when will they have planned the same number of rows ?

when rc = rt, of course.

so,

4h + 1 = 3h + 8

h = 7

4×7 + 1 = 28 + 1 = 29 rows

after 7 hours Quincy and his mom will each have planted 29 rows of vegetables.