Question

Q6 A brand of lemonade has a sugar content of 2.5 grams per 100 millilitres. A brand of apple juice has a sugar content of 12 grams per 100 millilitres. Work out the ratio in which this apple juice and lemonade should be mixed to produce a drink with a sugar content of 6 grams per 100 millilitres.​

Answer 1

• Apple juice : lemonade = 7 : 12

Explanation:

Let the amount of lemonade be x and apple juice be y.

The mixture has sugar content:

• 0.025x + 0.12y = 6

And total volume:

• x + y = 100

Solve the system by substitution:

• x = 100 - y

• 0.025(100 - y) + 0.12y = 6
• 2.5 - 0.025y + 0.12y = 6
• 0.095y = 3.5
• y = 3.5/0.095
• y = 7/0.19
• y = 700/19

Find x:

• x =
• 100 - 700/19 =
• (1900 - 700)/19 =
• 1200/9

We are looking for ratio y/x:

• y/x =
• 700/19 ÷ 1200/19 =
• 700/1200 =
• 7/12