If we multiply a number by 5/2 and add 2/3 to the product, we get -7/12. Find the number. Class 9

If we multiply a number by 5/2 and add 2/3 to the product, we get -7/12. Find the number. Class 9

Question 1.

If we multiply a number by $\frac{5}{2}$ and add $\frac{2}{3}$ to the product, we get $\frac{-7}{12}$. Find the number. Class 9

Solution:

Let the number be x.

According to the given condition,

$\begin{array}{ll} & \frac{5}{2} x+\frac{2}{3}=-\frac{7}{12} \\ \therefore & \frac{5}{2} x=-\frac{7}{12}-\frac{2}{3} \\ \therefore & \frac{5}{2} x=-\frac{7}{12}-\frac{8}{12}\end{array}$

$\begin{array}{ll}\therefore & \frac{5}{2} x=-\frac{15}{12} \\ \therefore & x=\frac{-15}{12} \times \frac{2}{5}=-\frac{1}{2}\end{array}$

∴ The number is $\frac{-1}{2}$.

Question 2.

A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers? Class 9

Solution:

Let the first numbers be x

∴ Second number = 5x

When 21 is added to both numbers, the new numbers are

x + 21 and 5x + 21.

According to the given condition,

5x + 21 = 2( x + 21)

∴ 5x + 21 = 2x + 42

∴ 5x - 2x = 42 - 21

∴ 3x = 21

∴ x = $\frac{21}{3}$

∴ x = 7

Second number = 5x

= 5 × 7 = 35

∴ The two numbers are 35 and 7.