# Iced tea mixture is 1. use  9 tbsp mix to 4 cups of water, Or 2. Use  7 tbsp mix to 5 cups of water. If I want a strong glass of iced tea do I use mix 1 or 2? Please help me explain.

May 23, 2018

2nd mixture to be used.

#### Explanation:

In mix 1,
Qty of tea in 4 cups is 1.9 tbsp.
Hence qty of tea in 1 cup is (1.9)/4 tbsp.

In mix 2,
Qty of tea in 5 cups is 2.7 tbsp
Hence qty of tea in 1 cup is (2.7)/5 tbsp.

Now comparing qty of tea in both cups :-$\frac{1.9}{4} : \frac{2.7}{5}$
Or, $\frac{1.9 \times 5}{4 \times 5} : \frac{2.7 \times 4}{5 \times 4}$[ to make the denominator equal.]
Or,$\frac{9.5}{20} : \frac{10.8}{20}$
Or, $9.5 : 10.8$
Here 2nd one is strong.
Hence to get a strong glass of iced tea 2nd mixture to be used.

May 23, 2018

First cup

#### Explanation:

If you do the cups as a ratio $1 : n$

First cup $9 : 4 \implies 1 : \frac{4}{9} = 1 : 0. \dot{4}$

Second cup $7 : 5 \implies 1 : \frac{5}{7} = 1 : 0.7$

In the first cup there is less than half a cup of water with each tablespoon of iced tea mix. In the second cup there is nearly three quarters of a cup of water with the same amount of iced tea mixture.

May 23, 2018

Mix $1$ is stronger

#### Explanation:

You need to compare the amount of mix with the amount of water.
The more mix that is used makes the tea stronger.

It is probably easier to compare them as decimals.

1. Compare Tblsp to cups: $\frac{9}{4} = 2.25$

2. Compare Tblsp to cups: $\frac{7}{5} = 1.4$

Mix 1 is stronger.

We could have seen that without using maths.

In mix 2, the amount of tea used is less, but more water is used, so the mix will be weaker.