Two foods with different cups-per-pound recommendations and one total cup amount signal a linear system: two equations about the same two unknowns. Write the cup total, then convert each brand’s cups into the weight that portion covers. Graph the equations in Desmos and read the coordinate for the brand requested, not the other brand.
Hints
- Hint 1
A rate compares two quantities. To find how many pounds a portion of food covers, use pounds divided by cups, then multiply by the number of cups of that brand. What does each portion cover?
- Hint 2
The dog weighs 46 pounds in all. The two portions together must cover that weight; don’t give the dog a full 46-pound recommendation of each brand, which would count its weight twice.
- Hint 3
An intersection is where two graphed equations meet, so its coordinates satisfy both conditions. Use the first coordinate for brand R, then compare it with the answer choices as fractions; the graphed coordinate may be rounded.
Step-by-step
Convert the rates and graph the system
Step 1Write the cup total
The dog’s R and S portions together are 3.2 cups, so . In Desmos, use for and for . Type ; Desmos draws the line of portions that meet the cup total.
- Step 2
Convert each portion to pounds covered
Brand R gives cups for pounds, so one cup covers pounds. Its cups cover pounds. Likewise, brand S’s cups cover pounds. Keep each brand’s cups with its own rate; reversing cups and pounds here would give cups per pound, not pounds covered.
- Step 3
Make the portions cover the dog’s weight
The pounds covered by the two portions add to the dog’s 46 pounds. They don’t each cover a separate 46-pound dog, so . Type this in Desmos as . Its line crosses the cup-total line, giving portions that meet both conditions.
- Step 4
Read the brand R coordinate
Click the intersection, where the lines cross. Desmos shows about . The first coordinate is , the brand R portion. Type ; Desmos displays , which rounds to that first coordinate. So the dog eats cups of brand R. Choice D.