Question 1/20: Set 5 - Try Out - Mathematical Reasoning (SNBT)

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Number 1

The price of $3$ belts and $2$ ties is $\text{Rp }100,000.00$ , while the price of $1$ belt and $3$ ties of the same kind is $\text{Rp }62,500.00$ . If Yunus buys $1$ belt and $1$ tie, then he has to pay ....

$\text{Rp }27,500.00$

$\text{Rp }32,500.00$

$\text{Rp }35,000.00$

$\text{Rp }37,500.00$

$\text{Rp }42,500.00$

Explanation

Let the price of one belt be $x$ and the price of one tie be $y$ . Based on the information provided, we can form the following system of linear equations:

3x + 2y = 100,000

x + 3y = 62,500

To find the values of $x$ and $y$ , we can use the elimination method. We will eliminate the variable $x$ by multiplying the second equation by $3$ so that the coefficient of $x$ becomes the same in both equations.

\begin{cases} 3x + 2y = 100,000 \\ x + 3y = 62,500 \quad (\times 3) \end{cases}

\Rightarrow \begin{cases} 3x + 2y = 100,000 \\ 3x + 9y = 187,500 \end{cases}

Next, we subtract the first equation from the modified second equation to solve for $y$ .

(3x + 9y) - (3x + 2y) = 187,500 - 100,000

7y = 87,500

y = \frac{87,500}{7}

y = 12,500

Having found $y = 12,500$ , we substitute this value into one of the original equations, for example $x + 3y = 62,500$ , to find $x$ .

x + 3(12,500) = 62,500

x + 37,500 = 62,500

x = 62,500 - 37,500

x = 25,000

Thus, the price of one belt is $\text{Rp }25,000.00$ and the price of one tie is $\text{Rp }12,500.00$ . Since Yunus wants to buy $1$ of each, the total amount he needs to pay is the sum of both prices.

x + y = 25,000 + 12,500 = 37,500

Therefore, Yunus has to pay $\text{Rp }37,500.00$ .

Command Palette

Number 1

Explanation