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12 Sep 2025, 10:26
Kudos
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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100% (03:39) correct
0% (00:00) wrong based on 1 sessions
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The ratio of programmers to scientists at a company was 8:5 in the year 2000 and 3:4 in the year 2010. If the total number of programmers and scientists at the company was 52 in the year 2000 and 196 in the year 2010, how many more scientists were at the company in 2010 than in 2000?
27 Sep 2025, 11:52
Kudos
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Explanation
Step 1: Interpret the year 2000 data
In 2000:
Programmers : Scientists = 8:5
Total employees (programmers + scientists) = 52
Sum of ratio parts \(= 8+5=13\)
Number of scientists in \(2000 = \frac{5}{13}×52=20\)
Number of programmers in \(2000 = \frac{8}{13}×52=32\)
Check: \(20+32=52.\)
Step 2: Interpret the year 2010 data
In 2010:
Programmers : Scientists =3:4
Total employees = 196
Sum of ratio parts = 3+4=7
Number of scientists in 2010 \(=\frac{4}{7}×196=112\)
Number of programmers in \(2010 = \frac{3}{7}×196=84\)
Check:
\(112+84=196.\)
Step 3: Find the difference in scientists between 2010 and 2000
Scientists in 2010 − Scientists in 2000 = 112−20=92.
Step 1: Interpret the year 2000 data
In 2000:
Programmers : Scientists = 8:5
Total employees (programmers + scientists) = 52
Sum of ratio parts \(= 8+5=13\)
Number of scientists in \(2000 = \frac{5}{13}×52=20\)
Number of programmers in \(2000 = \frac{8}{13}×52=32\)
Check: \(20+32=52.\)
Step 2: Interpret the year 2010 data
In 2010:
Programmers : Scientists =3:4
Total employees = 196
Sum of ratio parts = 3+4=7
Number of scientists in 2010 \(=\frac{4}{7}×196=112\)
Number of programmers in \(2010 = \frac{3}{7}×196=84\)
Check:
\(112+84=196.\)
Step 3: Find the difference in scientists between 2010 and 2000
Scientists in 2010 − Scientists in 2000 = 112−20=92.
