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Practice sheet · Cosmetics Path · Lens 1: Math

Percent & pH

Practice for The Math of Cosmetics: grams and millilitres, percent recipes, scaling, ratios, pH, unit price, SPF, shelf life and survey claims (pp.8–16), plus A1–A2 (pp.17–18).
Warm-upCoreLevel Up
Name Date Time I spent
Remember

Mass = volume × density. Percent recipe: each part = percent × batch. Scale factor = new batch ÷ old batch. Each pH step is 10× more or less acidic.

SPF: share blocked ≈ 1 − 1 ÷ SPF. PAO 12M = use within 12 months of opening. Patch-test anything new on a small spot, and make recipes only with an adult.

Warm-up

One step

Grams, percents and pH.
1

mL to g

An oil has density 0.92 g/mL. What is the mass of 80 mL?

2

Percent

A recipe is 30% shea butter. How many grams in an 80 g batch?

3

pH

How many times more acidic is pH 3 than pH 6?

4

Unit price

A 250 mL bottle costs $11. What is the price per mL, and per 100 mL?

Core

Two or three steps

Check the parts add to 100%.
5

Lip balm

A 50 g lip balm is 20% beeswax, 30% shea butter and 50% oil. How many grams of each?

6

Scale it

A sugar scrub uses 80 g sugar and 40 g oil. Scale it to a 300 g batch. What is the scale factor, and how much of each?

Cosmetics Practice · Cosmetics Path · Unizon1/2
Cosmetics Path · Unizon · PracticePercent, ratio & pH
7

Ratio

A salve is 1 part wax to 4 parts oil by mass. How much of each for 75 g?

8

SPF

About what share does SPF 25 block? What share gets through SPF 60? How does SPF 45 compare to SPF 15 for what gets through?

9

Shelf life

A cream opened in November 2026 shows 18M. Use it by when? A mascara opened the same month shows 3M?

10

Survey claims

“80% saw smoother skin!” in a survey of 25 people, versus 70% in a survey of 300. How many people is each? Which claim is stronger evidence?

Level Up

Equations

A1–A2 (pp.17–18).
11

Solve for grams

Butter costs $0.25 a gram plus $4 for a tin. Solve 0.25g + 4 = 19.

12

Two suppliers

Supplier A: $0.30 a gram plus $2 shipping. Supplier B: $0.18 a gram plus $8. When are they equal, and what does it cost?

13

pH, squared up

Skin is about pH 5.5; water is pH 7. How many times more acidic is skin? (10 to what power?)

14

Label

A rectangular label is 5 cm longer than it is wide, with an area of 84 cm². Solve w(w + 5) = 84.

Make your own problem

Your turn to be the cosmetic chemist

  1. Read the label on a product at home (don’t open or mix anything).
  2. Write a question about its percent, unit price, SPF or shelf life.
  3. Solve it, and ask what claim the label’s numbers really support.

My problem, and my worked answer:

Cosmetics Practice · Cosmetics Path · Unizon2/2
Cosmetics Path · Unizon · PracticePercent, ratio & pH

Try every problem first, then check here. Wrong answers are useful: find the step where your work and the key split apart.

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Answer key

Worked solutions. Prices, recipes and surveys are made-up examples. Make recipes only with an adult.

Warm-up
1
73.6 g 80 × 0.92 = 73.6.
2
24 g 0.30 × 80 = 24.
3
1,000× Three pH steps: 10 × 10 × 10 = 1,000.
4
$0.044 per mL · $4.40 per 100 mL 11 ÷ 250 = 0.044; × 100 = 4.40.
Core
5
10 g · 15 g · 25 g Each percent × 50 g. They add to 50.
6
× 2.5 · 200 g sugar · 100 g oil 300 ÷ 120 = 2.5. 80 × 2.5 = 200; 40 × 2.5 = 100.
7
15 g wax · 60 g oil 5 parts in all: 75 ÷ 5 = 15 g per part.
8
96% · ≈ 1.7% · a third as much 1 − 1/25 = 0.96. 1/60 ≈ 1.7% (98.3% blocked). 1/45 ≈ 2.2% vs 1/15 ≈ 6.7%: a third. Use enough and reapply (p.14).
9
May 2028 · February 2027 Count forward 18 months, then 3 months, from November 2026. Write the date on the product.
10
20 people · 210 people · the second A bigger sample is stronger evidence. Also ask: who paid for the survey, and smoother compared with what?
Level Up
11
60 g 0.25g = 15 → g = 60.
12
50 g · $17 0.12g = 6 → g = 50. 0.30 × 50 + 2 = 17. B is cheaper above 50 g.
13
≈ 31.6× 7 − 5.5 = 1.5 steps: 10¹·⁵ ≈ 31.6.
14
7 cm × 12 cm w² + 5w − 84 = 0 → (w + 12)(w − 7) = 0 → w = 7.
Make your own: write each part as a percent of the whole batch, check they add to 100%, and keep g and mL apart.
Cosmetics Practice · Cosmetics Path · UnizonAnswer key