2.2 Answer the following increasing and decreasing ratios: a) Increase \( 11,47 \mathrm{~kg} \) in the ratio of \( 11: 7 \) (2) \( \square \) b) Decrease R2 980 in the ratio of \( 5: 6 \) (2) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \)

We are given two problems—one in which a quantity is increased by an amount that is in a given ratio to the original, and one in which a quantity is decreased so that the remainder and the amount subtracted are in a given ratio. Before we begin, note that in these types of problems: • When a quantity is increased “in the ratio a : b” it typically means that the original quantity is to the increase as a is to b. Hence, if the original value is a parts and the increase is b parts, then the new total is (a + b) parts. In our case, the original is 11 parts and the increase is 7 parts, so total parts = 11 + 7 = 18. • When a quantity is decreased “in the ratio m : n” it is usually stated that after decreasing, the remaining part and the amount subtracted are in the ratio m : n. Hence, the remainder is m parts and the subtracted amount is n parts. The original number, therefore, is divided into m + n parts. Let’s now solve each part. ────────────────────────────── Problem (a): Increase 11.47 kg in the ratio 11 : 7 Interpretation: • The original amount (11.47 kg) corresponds to 11 parts. • The increase will be 7 parts. • Thus, the new total will have 11 + 7 = 18 parts. Step 1. Find the value of one part:   One part = (Original amount) / 11 = 11.47 ÷ 11     11.47 ÷ 11 = 1.043636… kg (approximately) Step 2. Find the new total:   New total = (18 parts) = 18 × (value of one part)     New total ≈ 18 × 1.043636… = 18.7849 kg Rounded suitably, the new total is approximately 18.78 kg. ────────────────────────────── Problem (b): Decrease R2,980 in the ratio 5 : 6 Interpretation: For a decrease the wording “in the ratio 5 : 6” is taken to mean that after the decrease the remaining part and the subtracted (decrease) part are in the ratio 5 : 6. That is,   Remaining part : Amount subtracted = 5 : 6 Thus, the original amount is divided into 5 + 6 = 11 parts, where the remaining (after decrease) is 5 parts. Step 1. Find the value of one part:   One part = Total (R2,980) ÷ 11     One part = 2980 ÷ 11 ≈ 270.91 rupees Step 2. Find the new (reduced) value:   New value = (Remaining parts) = 5 parts = 5 × (value of one part)     New value ≈ 5 × 270.91 = 1354.55 rupees Thus, after the decrease the resulting amount is approximately R1,354.55. ────────────────────────────── Final Answers: a) After increasing 11.47 kg in the ratio 11 : 7, the new total is approximately 18.78 kg. b) After decreasing R2,980 in the ratio 5 : 6, the new amount is approximately R1,354.55. These are your answers to the given problems.