Question 19996

Nov 23, 2017

Under $40$ years group has a higher ratio of black-tea
drinkers to herbal-tea drinkers .

Explanation:

Over $40$ years group the ratio of black-tea drinkers to herbal-

tea drinkers is $600 : 1500 = 6 : 15 = 2 : 5 = 18 : 45$

Under $40$ years group the ratio of black-tea drinkers to herbal-

tea drinkers is $1400 : 1800 = 14 : 18 = 7 : 9 = 35 : 45$

$\therefore 35 : 45 > 18 \cdot 45$

So under $40$ years group has a higher ratio of black-tea drinkers

to herbal-tea drinkers . [Ans]

Nov 23, 2017

The under-40 group had a higher ratio (78%) than the over-40 group (40%) of black tea to herbal tea drinkers

Explanation:

This is a Ratio and Proportion problem

Set up the ratios and give them a common decimal denominator so they can be compared

$$                      Over 40       Under 40


$\frac{b l a c k}{h e r b a l} . . . . . \frac{600}{1500} . . . . . \frac{1400}{1800}$

1) Reduce the fractions as far as possible

$\frac{b l a c k}{h e r b a l} . . . . . . \frac{6}{15} . . . . . . . \frac{14}{18}$

$\frac{b l a c k}{h e r b a l} . . . . . . . \frac{2}{5} . . . . . . . . \frac{7}{9}$

2) Determine which fraction is larger by making them both into decimals and percents

Over 40: 2/5 = 0.4 = 40% prefer black tea to herbal tea

Under 40: 7/9 = 0.78 = 78% prefer black tea to herbal tea

Among people  over  40, 40% drink black tea
Among people under 40, 78%# drink black tea