Question
1.2 R126,00 decreased in the ratio \( 3: 7 \) is .... A. R37,80 B. R12,60 C. R294 D. R54
Ask by Rojas Tran. in South Africa
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The amount decreased is R37,80.
Solution
We are told that when R126,00 is decreased, the amount by which it is decreased and what remains are in the ratio 3:7. In other words, if d is the decrease and r is the remaining amount, then
d : r = 3 : 7
Since the total amount is the sum of these two parts, we have
d + r = R126,00
Step 1. Express r in terms of d using the ratio:
d / r = 3/7 ⟹ r = (7/3)·d
Step 2. Substitute r into the total:
d + (7/3)·d = 126
(1 + 7/3)·d = 126
(3/3 + 7/3)·d = 126
(10/3)·d = 126
Step 3. Solve for d:
d = 126 × (3/10)
d = 378/10
d = R37,80
Thus, the amount by which R126,00 is decreased in the ratio 3:7 is R37,80.
The correct answer is Option A.
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Simplify this solution Bonus Knowledge
To solve the problem, first, determine how much R126,00 is decreased by using the ratio \( 3:7 \). The total parts of the ratio are \( 3 + 7 = 10 \). The decrease represented by the \( 3 \) parts will be: \[ \text{Decrease} = \frac{3}{10} \times R126,00 = R37,80 \] So, the answer is A. R37,80. Now that you know the decrease, you can find the amount remaining by subtracting the decrease from the original amount: \[ \text{Remaining amount} = R126,00 - R37,80 = R88,20 \] The ratio \( 3:7 \) shows a neat division—so you are left with a clear picture of how a decrease impacts the whole!
