Can you explain a more direct way to solve College Board Official Practice Test 9, Math Section 4 #19, than the College Board’s explanation? I seem to remember something about making a chart to solve mixture problems. Would that work here?

I’ll tell you how I thought about it, hopefully it’ll be helpful. First, the original data you’re given says Crunch Grain (i’m just going to call it “Crunchy”) has 210 calories in 3/4 cup. Question 19 tells you that Super Grain (just “Super” from here on out) has 240 calories in 1 cup.

Just for comparison’s sake, my first instinct was to break Super into quarter cups. If it’s got 240 calories in 1 cup, it has 60 calories per 1/4 cup.

Oh, convenient! 3/4 cup of Crunchy has 210 calories, and 1/4 cup of Super has 60 calories. We want 1 cup with 270 calories, so just doing that first step actually got me where I wanted to go! This is going to be a mix of 3/4 cup Crunchy with 1/4 cup Super. The answer is B.

Now, you asked about a chart. As you can see, I didn’t use one here, but if I hadn’t just stumbled upon the answer, I probably would have set up a backsolving chart using the answer choices.

Cups Super | Cups Crunchy | Calories Super | Calories Crunchy | Total Calories |

1/8 | 7/8 | |||

1/4 | 3/4 | 60 | 210 | 270 |

1/3 | 2/3 | |||

1/2 | 1/2 |

I’ve filled it out only for the right answer but for each other answer you can use ratios to figure out how many calories are in those different measurements.

Note that once I set up that chart, I definitely would have tried choice B first anyway, because I would have noted that I don’t need to do any calculations on Crunchy for choice B: I already know there are 210 calories in 3/4 cup of Crunchy.

Hope that helps!

## Comments (1)

Thanks, Mike!