A comparison between two days and a combined total is a cue to build a linear equation, one with the unknown only to the first power. Let a letter count the day the question asks about, express the other day using that letter, and add the counts. Enter the equation into Desmos as a regression. Don’t submit the other day’s count.
Hints
- Hint 1
Use one variable, a letter for an unknown count, for the day the question asks about. “80 fewer than 1.5 times” means multiply that count first, then subtract 80. What expression counts the second day?
- Hint 2
An equation says two quantities are equal. Add the first-day count and your second-day expression to get 520 gadgets. Keep the subtraction in the second-day expression: what equation matches the total?
Step-by-step
Write one equation for both days
Step 1Express the second day using the first
Let the variable count gadgets made on the first day. The second day made times that count, then fewer, so its count is . Writing would subtract before multiplying, which changes the count.
- Step 2
Add the two days to get the total
The two days together produced gadgets, so add their counts:
Write both parts of a total using the same variable before adding them.
- Step 3
Solve for the first-day count
Type . In this regression, is the number Desmos finds, and tells it to make the two sides equal. Under PARAMETERS, Desmos shows . Since counts the first day’s gadgets, the factory produced 240 gadgets on the first day. Grid in 240.