Let's break down Malik's solution step by step and identify where he made his first error in solving the equation [tex]\(\frac{2}{5} x - 4y = 10\)[/tex] when [tex]\(y = 60\)[/tex]:
1. Starting Equation:
[tex]\[
\frac{2}{5} x - 4 y = 10
\][/tex]
2. Substitute [tex]\(y = 60\)[/tex]:
[tex]\[
\frac{2}{5} x - 4(60) = 10
\][/tex]
3. Simplify the substitution:
[tex]\[
\frac{2}{5} x - 240 = 10
\][/tex]
4. Add 240 to both sides to isolate [tex]\(\frac{2}{5} x\)[/tex]:
[tex]\[
\frac{2}{5} x - 240 + 240 = 10 + 240
\][/tex]
[tex]\[
\frac{2}{5} x = 250
\][/tex]
5. Multiply both sides by [tex]\(\frac{5}{2}\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[
\left(\frac{5}{2}\right)\left(\frac{2}{5} x\right) = \left(\frac{5}{2}\right)(250)
\][/tex]
[tex]\[
x = 625
\][/tex]
Now, we see that there is a discrepancy between Malik's result and the correct calculation. Let’s pinpoint the error in Malik's work:
- At the last step, Malik wrote:
[tex]\[
\left(\frac{5}{2}\right)(250)
\][/tex]
- Malik concluded:
[tex]\[
x = 265
\][/tex]
The correct multiplication should be:
[tex]\[
\left(\frac{5}{2}\right) \times 250 = \frac{5 \times 250}{2} = \frac{1250}{2} = 625
\][/tex]
Hence, the first error Malik made was in the computation of:
[tex]\[
\left(\frac{5}{2}\right) \times 250
\][/tex]
Malik did not multiply [tex]\(\left(\frac{5}{2}\right)(250)\)[/tex] correctly.
