Jared and Ronald are both selling cookie dough for a fundraiser. Although Jared has already sold 10 tubs, Ronald hasn't sold any yet. If Jared starts selling 7 tubs per day and Ronald begins selling 8 tubs per day, they will eventually sell the same amount of cookie dough. How many tubs will each sell?Write a system of equations, graph them, and type the solution.1020304050204060801000xyDaysTubsJaredRonald
Question
Jared and Ronald are both selling cookie dough for a fundraiser. Although Jared has already sold 10 tubs, Ronald hasn't sold any yet. If Jared starts selling 7 tubs per day and Ronald begins selling 8 tubs per day, they will eventually sell the same amount of cookie dough. How many tubs will each sell?Write a system of equations, graph them, and type the solution.1020304050204060801000xyDaysTubsJaredRonald
Solution
The problem can be solved by setting up a system of linear equations.
Let's denote:
- J as the number of tubs Jared sells,
- R as the number of tubs Ronald sells,
- d as the number of days.
From the problem, we know that Jared has already sold 10 tubs and sells 7 more each day, so his total sales can be represented as:
J = 10 + 7d
Ronald hasn't sold any tubs yet but sells 8 each day, so his total sales can be represented as:
R = 8d
Since we know that eventually they will sell the same amount of cookie dough, we can set these two equations equal to each other:
10 + 7d = 8d
Solving this equation for d gives us:
d = 10
Substituting d = 10 into the equations for J and R gives us:
J = 10 + 710 = 80 R = 810 = 80
So, both Jared and Ronald will each sell 80 tubs of cookie dough.
To graph these equations, you would plot the lines J = 10 + 7d and R = 8d on the same graph. The point where these two lines intersect represents the solution to the system of equations. In this case, the lines would intersect at the point (10, 80), confirming that after 10 days, both Jared and Ronald will have sold 80 tubs of cookie dough.
Similar Questions
On one trip to the store, Heather bought 22 boxes of crackers and 88 packages of cheese for $23$23. On another trip to the store, she bought 88 boxes of crackers and 55 packages of cheese for $52$52.She determined the system of equations that represents the situation. 2x+8y=232𝑥+8𝑦=238x+5y=528𝑥+5𝑦=52 She graphed the equations, as shown. Assume the price for each item stays the same between visits. Between which 22 integers is the price of each item, in dollars?Enter your answer in each box.Price of box of crackers: Between $ and $Price of package of cheese: Between $ and $
Beth made wristbands and belts for a craft sale. She sold 30 of these items. Each wristband sold for $5.50. Each belt sold for $8.75. If Beth made $204 at the craft sale, how many wristbands did she sell? How many belts did she sell? Write and solve a system of equations to solve the problem. Show your work
Christian went into a movie theater and bought 8 drinks and 10 candies, costing a total of $94. Dianelys went into the same movie theater and bought 9 drinks and 6 candies, costing a total of $79.50. Write a system of equations that could be used to determine the price of each drink and the price of each candy. Define the variables that you use to write the system.
A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y? A. 4y=3x+644𝑦=3𝑥+648y=x+688𝑦=𝑥+68 B. 4y=3x+644𝑦=3𝑥+648y=x+608𝑦=𝑥+60 C. 3x+4y=643𝑥+4𝑦=64x+8y=68𝑥+8𝑦=68 D. 3x+4y=643𝑥+4𝑦=64x+8y=60
Mason and his children went into a movie theater and he bought $36.50 worth of candies and pretzels. Each candy costs $4.25 and each pretzel costs $3.50. He bought 6 more pretzels than candies. Write a system of equations that could be used to determine the number of candies and the number of pretzels that Mason bought. Define the variables that you use to write the system.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.