standard_description: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
problem_activity: Hummingbird feeders can be filled with a simple sugar water mixture. Two different recipes are shown below.
|                  |   Water (cups)   | Sugar (cups) | $$2$$ | $$\frac{1}{2}$$ | $$4$$ | $$1$$ | $$16$$ | $$4$$ | $$28$$ | $$7$$ | $$32$$ | $$8$$ |   | Water (cups) | Sugar (cups) | $$2\frac{2}{3}$$ | $$1$$ | $$4$$ | $$1\frac{1}{2}$$ | $$8$$ | $$3$$ | $$24$$ | $$9$$ | $$32$$ | $$12$$ |
|------------------|------------------|--------------|-------|-----------------|-------|-------|--------|-------|--------|-------|--------|-------|---|--------------|--------------|------------------|-------|-------|------------------|-------|-------|--------|-------|--------|--------|
|   Water (cups)   |   Sugar (cups)   |              |       |                 |       |       |        |       |        |       |        |       |   |              |              |                  |       |       |                  |       |       |        |       |        |        |
|      $$2$$       | $$\frac{1}{2}$$  |              |       |                 |       |       |        |       |        |       |        |       |   |              |              |                  |       |       |                  |       |       |        |       |        |        |
|      $$4$$       |      $$1$$       |              |       |                 |       |       |        |       |        |       |        |       |   |              |              |                  |       |       |                  |       |       |        |       |        |        |
|      $$16$$      |      $$4$$       |              |       |                 |       |       |        |       |        |       |        |       |   |              |              |                  |       |       |                  |       |       |        |       |        |        |
|      $$28$$      |      $$7$$       |              |       |                 |       |       |        |       |        |       |        |       |   |              |              |                  |       |       |                  |       |       |        |       |        |        |
|      $$32$$      |      $$8$$       |              |       |                 |       |       |        |       |        |       |        |       |   |              |              |                  |       |       |                  |       |       |        |       |        |        |
|   Water (cups)   |   Sugar (cups)   |              |       |                 |       |       |        |       |        |       |        |       |   |              |              |                  |       |       |                  |       |       |        |       |        |        |
| $$2\frac{2}{3}$$ |      $$1$$       |              |       |                 |       |       |        |       |        |       |        |       |   |              |              |                  |       |       |                  |       |       |        |       |        |        |
|      $$4$$       | $$1\frac{1}{2}$$ |              |       |                 |       |       |        |       |        |       |        |       |   |              |              |                  |       |       |                  |       |       |        |       |        |        |
|      $$8$$       |      $$3$$       |              |       |                 |       |       |        |       |        |       |        |       |   |              |              |                  |       |       |                  |       |       |        |       |        |        |
|      $$24$$      |      $$9$$       |              |       |                 |       |       |        |       |        |       |        |       |   |              |              |                  |       |       |                  |       |       |        |       |        |        |
|      $$32$$      |      $$12$$      |              |       |                 |       |       |        |       |        |       |        |       |   |              |              |                  |       |       |                  |       |       |        |       |        |        |
Compare the two different recipes. Which recipe is more sugary? Justify your response.


aligns: no