Question 109·Easy·Linear Inequalities in One or Two Variables
A bakery sells each cookie for $2 and wants to make at least $50 in cookie sales today. If the bakery has already made $34 from cookie sales, what is the minimum number of additional cookies it must sell to meet its goal?
For inequality word problems, always start by defining a variable for the unknown quantity (here, the number of additional cookies) and then translate the words into an inequality using phrases like "at least" () or "at most" (). Combine what you already have with what you still need, write an expression for the new total, and set it compared to the goal. Solve the inequality as you would a regular equation, then interpret the result in context, making sure to choose the smallest whole number that satisfies the inequality when dealing with countable items like cookies.
Hints
Figure out how much money is still needed
The bakery wants at least $50 and already has $34. How many more dollars do they need to reach $50?
Relate the needed money to cookies
Each cookie makes $2. If is the number of additional cookies, how can you write an expression for the extra money earned? Set this greater than or equal to the amount still needed.
Form and solve the inequality
Your inequality should look like (some number). Solve this inequality for and remember must be a whole number of cookies.
Choose the minimum whole number
From your inequality, pick the smallest whole number value of that makes the inequality true. That is the number of additional cookies needed.
Desmos Guide
Enter the total sales expression
In Desmos, type y = 2x + 34. This represents the total amount of money the bakery will have after selling additional cookies.
Add a reference line for the goal
Type a second equation: y = 50. This is the goal line showing $50 in sales.
Find the minimum x-value that meets the goal
Look at where the line reaches or goes above the line . Use a table (tap the gear icon and select "Table" for the first equation) and find the smallest -value where the corresponding -value is at least 50; that is the minimum number of additional cookies needed.
Step-by-step Explanation
Define the variable and write the inequality
Let be the number of additional cookies the bakery still needs to sell.
Each cookie brings in $2, and the bakery already has $34 in sales, so the total money after selling more cookies is
They want at least $50, which means the total must be greater than or equal to 50:
Isolate the variable term
Solve the inequality step by step.
First, subtract $34 from both sides to get the money still needed in terms of :
Solve for the minimum number of cookies
Now divide both sides of by 2:
This means the bakery must sell at least 8 more cookies to reach its goal, so the minimum number of additional cookies it must sell is 8.