Unit 2, Lesson 8
Which Variable to Solve for? (Part 1)
Algebra 1
Practice
Problem 1
Priya is buying raisins and almonds to make trail mix. Almonds cost \$5.20 per pound and raisins cost \$2.75 per pound. Priya spent \$11.70 buying almonds and raisins. The relationship between pounds of almonds \(a\), pounds of raisins \(r\), and the total cost is represented by the equation \(5.20a+2.75r=11.70\).
How many pounds of raisins did Priya buy if she bought the following amounts of almonds:
- 2 pounds of almonds
- 1.06 pounds of almonds
- 0.64 pounds of almonds
- \(a\) pounds of almonds
Problem 2
Here is a linear equation in two variables: \(2x+4y-31=123\).
Solve the equation, first for \(x\) and then for \(y\).
Problem 3
A chef bought \$17.01 worth of ribs and chicken. Ribs cost \$1.89 per pound and chicken costs \$0.90 per pound. The equation \(0.9c+1.89r=17.01\) represents the relationship between the quantities in this situation.
Show that each of the following equations is equivalent to \(0.9c+1.89r=17.01\). Then, explain when it might be helpful to write the equation in these forms.
- \(c = 18.9 - 2.1r\)
- \(r=\text-\frac{10}{21}c +9\)