Different bag sizes and two totals signal a linear system: two equations about the same two unknown bag counts. Convert both bag weights to the same unit, then write one equation for pounds and one for dollars. Graph both in Desmos and click their intersection. Match each coordinate to its bag type; taking the other coordinate answers a different question.
Hints
- Hint 1
Use pounds for both bag weights before writing the total-weight equation. The almonds come in ounces, so divide their ounces by the given ounces per pound. What does one almond bag weigh in pounds?
- Hint 2
Name the numbers of almond and cashew bags separately. A system means two equations about the same unknowns: one counts pounds, and the other counts dollars. Which price multiplies the almond-bag count?
- Hint 3
In Desmos, each equation graphs as a line; their intersection is the pair that makes both totals true. The almond count is the coordinate you assigned to almond bags, not the other coordinate or the sum.
Step-by-step
Convert units, then graph the two totals
Step 1Convert an almond bag to pounds
There are ounces in a pound, so one -ounce almond bag weighs pound. Convert before adding weights; the cashew bags are already measured in pounds.
- Step 2
Write the weight equation
Let count almond bags and count cashew bags. Each almond bag contributes pound and each cashew bag contributes pounds, so the weight total is . Every term in this equation measures pounds.
- Step 3
Write the cost equation
Multiply each bag count by its own price. The shop spends $138, so the dollar total is . The stays with almonds, which counts.
- Step 4
Read the almond count at the intersection
Type and on separate Desmos lines, then click where they cross. Desmos shows . This intersection satisfies both totals. Since counts almonds, the first coordinate means the shop buys bags of almonds. Choice B.