Office Supply Store M sells packs of printer paper for $4.75 each and ink cartridges for $6.25 each. Office Supply Store N sells packs of printer paper for $5.50 each and ink cartridges for $5.20 each. A particular purchase of printer paper packs and ink cartridges would cost $74.00 at Store M or $75.50 at Store N.
How many packs of printer paper are in this purchase?
Two stores pricing the same purchase give two conditions on two unknown counts, a system of linear equations. Let count the item asked for and count the other item. Write a cost equation for each store, then graph both in Desmos and click their intersection. The trap is reading the other coordinate as the requested count.
Hints
- Hint 1
A variable stands for a count you don't know yet. Let count paper packs and count ink cartridges. That makes the first coordinate of a Desmos point the paper count.
- Hint 2
Each store charges a price per item. Multiply the paper price by and the ink price by , then add them to get that store's total cost. What total does each store give?
- Hint 3
The equations describe the same purchase, so a solution to the system must satisfy both. Graph the equations, click where their lines cross, and read the coordinate for paper packs.
Step-by-step
Graph the two cost equations
Step 1Write Store M's cost equation
Let be the number of paper packs and the number of ink cartridges. At Store M, paper costs $4.75 per pack, so its paper bill is . Ink costs $6.25 each, so its ink bill is . Add the bills to match the total cost. Type in Desmos; it graphs the purchases that cost $74 at M.
- Step 2
Write Store N's cost equation
It's the same purchase at Store N, so keep for paper packs and for cartridges. Add its $5.50-per-pack paper bill and $5.20-per-cartridge ink bill to match $75.50. Type below the first line. These two equations form a system: both must be true for the purchase.
- Step 3
Read the paper-pack count
Click the intersection, where both lines meet. Desmos labels it , meaning paper packs and ink cartridges. The first coordinate answers the question; counts ink, not paper. Match the requested item to its coordinate before answering. The purchase contains packs of printer paper. Choice C.