A farmer buys bags of corn seed and bags of fertilizer for his fields. One purchase of bags of corn seed and bags of fertilizer costs a total of dollars. Another purchase of bags of corn seed and bags of fertilizer costs a total of dollars. What is the cost, in dollars, of one bag of fertilizer?
Two different purchases involving the same items signal a system of linear equations: the unknown prices must fit both totals. Give each item a per-bag price and write one equation for each purchase. Then graph both equations in Desmos and click their intersection. The trap is reading the seed price instead of the fertilizer price the question asks for.
Hints
- Hint 1
A variable is a letter for a number you don't know. Let be the price of one seed bag and the price of one fertilizer bag. For the first purchase, which bag counts multiply those per-bag prices?
- Hint 2
A system is two equations that must both be true. Write a separate equation for the second purchase using the same prices, and . Where their graphs cross, which coordinate will give you the fertilizer price?
Step-by-step
Graph the two purchase equations
Step 1Write the first purchase as a cost equation
Let be the price of one seed bag and the price of one fertilizer bag. The first purchase has seed bags and fertilizer bags, so its total cost is . Each term counts dollars, not bags.
- Step 2
Write the second purchase with the same prices
The prices per bag haven't changed. The second purchase has seed bags and fertilizer bags, so its separate cost equation is . Keep with seed and with fertilizer in both equations.
- Step 3
Read the fertilizer price at the intersection
Type and on separate Desmos lines. Click the intersection, the point on both lines. Desmos shows . The second coordinate is , so one bag of fertilizer costs $20.50. Choice C.