Splitting a Total in a Ratio
Question
Answer choices
- 180
- 115
- 300
- 125
- 120
E Correct answer: E) 120
Set up the problem carefully before computing. Add the ratio parts (4 + 6 = 10) to find how many equal pieces the total breaks into. Each piece equals 300 ÷ 10 = 30 dollars. The first person gets 4 pieces × 30 = 120 dollars.
Carry the arithmetic through one step at a time, double-checking signs and units. The ACT writes wrong answers to catch the most common slips, so an answer that "looks right" without verification is risky.
Plug the answer back into the original expression as a sanity check whenever the problem allows. If the substitution does not balance, you have made an arithmetic mistake earlier in the work.
The underlying rule
When you split a total in a ratio of 4:6, the parts add to 10. The first person gets 4/10 of the total. So 4/10 × 300 = 120.
Why each wrong answer is wrong
- A) 180: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- B) 115: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- C) 300: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) 125: A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
On any "split in a ratio" problem, first add the ratio parts to find one share. Then multiply by the number of shares the question asks about.
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