Question

The investments made by family and friends in a family business is $\$$($\frac{11}{3}$x + 52) and $\$$($\frac{7}{3}$x + 81) respectively.

Calculate the total funds invested (in $\$$) in the business ?

• A. $\$$($\frac{17}{3}$x + 133)
• B. $\$$(6x + 122)
• C. $\$$(6x + 133)
• D. $\$$($\frac{19}{3}$x + 133)

Answer 1

The correct option is C $\$$(6x + 133)

Given:
Investment by family = $\$$($\frac{11}{3}$x + 52)
Investment by friends = $\$$($\frac{7}{3}$x + 81)

Let’s add the two linear expressions using properties of expression to calculate total investment.

Using commutative property:
$\frac{11}{3}$x + $\frac{7}{3}$x + 52 + 81


Using associative property:
= ($\frac{11}{3}$x + $\frac{7}{3}$x) + 52 + 81

= ($\frac{18}{3}$x) + 133

= 6x + 133

Therefore, the total funds invested is
$\$$(6x + 133).