Question 16/20: Set 2 - Try Out - Mathematical Reasoning (SNBT)

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Mr. Budi works for $6$ days with $4$ days of overtime and earns $\text{Rp}74,000.00$ . Mr. Agus works for $5$ days with $2$ days of overtime and earns $\text{Rp}55,000.00$ . If Mr. Dani works for $5$ days and does overtime continuously (every day), the wage he will earn is...

$\text{Rp}60,000.00$

$\text{Rp}65,000.00$

$\text{Rp}67,000.00$

$\text{Rp}70,000.00$

$\text{Rp}75,000.00$

Explanation

Modeling the Problem into Equations

Let $x$ be the daily wage and $y$ be the overtime wage. Based on the given information, we can form a system of linear equations with two variables:

6x + 4y = 74,000 \quad \dots (1)

5x + 2y = 55,000 \quad \dots (2)

Equation $(1)$ comes from Mr. Budi working $6$ days with $4$ overtime days, while equation $(2)$ comes from Mr. Agus working $5$ days with $2$ overtime days.

Solving the System of Equations

First, simplify equation $(1)$ by dividing both sides by $2$ :

3x + 2y = 37,000 \quad \dots (3)

Now we have two simpler equations:

5x + 2y = 55,000 \quad \dots (2)

3x + 2y = 37,000 \quad \dots (3)

We can eliminate variable $y$ by subtracting equation $(3)$ from equation $(2)$ :

(5x + 2y) - (3x + 2y) = 55,000 - 37,000

2x = 18,000

x = 9,000

After finding $x = 9,000$ , substitute it into equation $(3)$ to find $y$ :

3(9,000) + 2y = 37,000

27,000 + 2y = 37,000

2y = 10,000

y = 5,000

So, the daily wage is $\text{Rp}9,000.00$ and the overtime wage is $\text{Rp}5,000.00$ .

Calculating Mr. Dani's Wage

Mr. Dani works for $5$ days and does overtime continuously, which means he has $5$ regular work days and $5$ overtime days. The wage he earns is:

5x + 5y = 5(9,000) + 5(5,000)

= 45,000 + 25,000

= 70,000

Alternatively, we can factor the equation:

5(x + y) = 5(9,000 + 5,000)

= 5(14,000)

= 70,000

Thus, the wage Mr. Dani will earn is $\text{Rp}70,000.00$ .

Command Palette

Number 16

Explanation