At the bakery shop, each baker works at his or her own speed, making the same number of cakes each day. Marissa makes 28 cakes in 2 weeks, Carlos makes 60 cakes in 20 days, and Shelby makes 5 cakes in 2 days. When the shop owner graphs the relationship between the number of cakes made and days, who has the steepest graph? Explain.
To determine who has the steepest graph, we need to find the rate at which each baker makes cakes.
For Marissa:
She makes 28 cakes in 2 weeks, which is equivalent to 14 cakes per week. Therefore, her rate of making cakes is 14/7 = 2 cakes per day.
For Carlos:
He makes 60 cakes in 20 days. Therefore, his rate of making cakes is 60/20 = 3 cakes per day.
For Shelby:
She makes 5 cakes in 2 days. Therefore, her rate of making cakes is 5/2 = 2.5 cakes per day.
Now, comparing the rates of making cakes, we can see that Carlos has the steepest graph. This is because Carlos makes the highest number of cakes per day, with a rate of 3 cakes per day, compared to Marissa's rate of 2 cakes per day and Shelby's rate of 2.5 cakes per day. The steeper the graph, the greater the rate of cake production.
To determine who has the steepest graph, we need to calculate the rate at which each baker produces cakes. The steeper the graph, the higher the rate of cake production.
First, let's calculate the rate of cake production for each baker:
Marissa makes 28 cakes in 2 weeks. We can calculate her rate of cake production by dividing the number of cakes (28) by the number of days it took her to make them (14 days in 2 weeks). So, Marissa's rate is 28 cakes / 14 days = 2 cakes per day.
Carlos makes 60 cakes in 20 days. His rate of cake production is calculated by dividing the number of cakes (60) by the number of days it took him (20 days). So, Carlos' rate is 60 cakes / 20 days = 3 cakes per day.
Shelby makes 5 cakes in 2 days. To calculate the rate of cake production for Shelby, we divide the number of cakes (5) by the number of days it took her (2 days). Shelby's rate is 5 cakes / 2 days = 2.5 cakes per day.
Now, let's compare the rates of cake production:
Marissa: 2 cakes per day
Carlos: 3 cakes per day
Shelby: 2.5 cakes per day
Among the three bakers, Carlos has the highest rate of cake production, making 3 cakes per day. Therefore, when the shop owner graphs the relationship between the number of cakes made and days, Carlos will have the steepest graph.
Just find the unit rate for each person.
Marissa's rate = 28 cakes/ 2 weeks = 28/14 cakes per day = 2 cakes/day
Carlos' rate = 60 cakes/20 days = 3 cakes/day
Shelby's rare = 5 cakes/2 days = 2/5 cakes/day
How do you think this relates to the steepness of the graphs ?