Linear Word Problems for Kids: Starting Cost Plus a Rate (Grade 8 Math)

Hi, I'm Luna from DoodleBeez. Today we are solving linear word problems. Many real costs have two parts: a starting amount you pay once, and a rate you pay again and again for each one.

Renting a bike costs five dollars to start, plus three dollars for every hour. The rate is three, and it goes with x, the number of hours. The starting amount is five. So y equals three x plus five.

How much for four hours? Put four in for x. Three times four is twelve. Twelve plus five is seventeen. Renting the bike for four hours costs seventeen dollars.

We can also work backwards. Sam paid twenty six dollars. How many hours did Sam ride? Take away the five dollar start to get twenty one. Then divide by three. Sam rode for seven hours.

On a graph, the starting amount is where the line crosses the y axis. We call it the y intercept. The rate is the slope, how much the line climbs for each step to the right.

Watch for the clue words. Words like per, each and every point to the rate. Words like fee, to start, or one time point to the starting amount. Find those two, and the equation almost writes itself.

Now it's your turn. A gym charges ten dollars to join, plus four dollars per visit. How much for six visits? Pause and try. The equation is y equals four x plus ten. Four times six is twenty four, plus ten is thirty four dollars.

Great job! Remember, find the rate and the starting amount. The rate goes with x, and the start is added on. Work backwards to find x. Practice linear word problems in Middle School Math at doodlebeez.com. See you next time!