Question

If investments made by a person and his friends in a business is $\frac{7}{6}$x + 78 and $\frac{13}{6}$x + 54 respectively, the total funds invested is .

• A. $\frac{20}{3}$x + 132
• B. $\frac{10}{3}$x + 122
• C. $\frac{10}{3}$x + 132
• D. $\frac{20}{3}$x + 122

Answer 1

The correct option is C $\frac{10}{3}$x + 132

Given:
Investment by person = $\frac{7}{6}$x + 78
Investment by friends = $\frac{13}{6}$x + 54

Let’s add the two linear expressions using properties of expression to calculate total investment.
$\Rightarrow$ ($\frac{7}{6}$x + 78) + ($\frac{13}{6}$x + 54)

Using commutative property:
$\Rightarrow$ $\frac{7}{6}$x + $\frac{13}{6}$x + 78 + 54

Using associative property:
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\Rightarrow$ ($\frac{7}{6}$x + $\frac{13}{6}$x) + (78 + 54)

= $\frac{20}{6}$x + 132

= $\frac{10}{3}$x + 132

$\therefore$ Total funds invested in the business is $\frac{10}{3}$x + 132.