A system of equations is two equations that must hold at the same time. In a word problem with two counts and two facts, translate each fact separately: a comparison tells you how the counts differ, and a total tells you what to add. Keep track of which count is larger; reversing the comparison describes a different situation.
Hints
- Hint 1
The phrase more blue than red tells you which count is larger. Start with the red count and add the extra pens. Which letter should equal that result?
- Hint 2
A total counts every pen once. Red pens and blue pens make up all the pens in the box, so how should you combine their counts to get 42?
Step-by-step
Translate each fact
Step 1Write the comparison
No Desmos needed. The task is to translate the words, not solve for the counts. The blue count is larger: start with the red count and add to get the blue count . So . Writing would make red the larger count.
- Step 2
Write the total and match the system
The 42 pens in total include both colors, so add their counts: . Both facts must hold at once, so the system is and . Choice D.