Two types of items and two totals point to a system of equations: one equation counts items, and the other counts dollars. Assign a variable to each type, graph both equations in Desmos, and click their intersection. Keep item counts and dollar amounts in separate equations, then read the coordinate for the item the question asks about.
Hints
- Hint 1
Let count bracelets and count keychains. An equation for the item total adds the two counts without using prices. What should equal?
- Hint 2
A system uses two equations that must both be true. Multiply each price by the number of that item, then add the dollar amounts. Which total should they equal?
- Hint 3
The intersection of the two graphed equations fits both totals. If counts keychains, read the second coordinate of that point, not the first.
Step-by-step
Graph the two totals
Step 1Write the item-count equation
Let count bracelets and count keychains. The 7 items are all one kind or the other, so their counts add to .
- Step 2
Write the cost equation
The bracelets cost dollars and the keychains cost dollars, so the $17 spent gives . This and form a system, two equations that must both hold. Don't put on the right here: it counts items, not dollars.
- Step 3
Read the keychain count
Type and on separate Desmos lines. Click their intersection, where both equations are true. Desmos shows . The second coordinate is , so Lena bought keychains. Choice C.