Question

write an expression for each situation. then simplify.
lola has 5 more than 6 times as many homework problems as ronald.
mohamad has six less than twice the amount ronald has.

1. write the expression for the amount of homework problems lola has.
2. write the expression for the amount of homework problems mohamad has.
3. write and simplify the expression for the product of lolas and mohamads homework problems.

Explanation:

Sub - question 1

Step1: Define variable for Ronald's problems

Let the number of homework problems Ronald has be $x$.

Step2: Translate Lola's situation to expression

Lola has 5 more than 6 times as many as Ronald. 6 times Ronald's problems is $6x$, and 5 more than that is $6x + 5$.

Step1: Use the same variable for Ronald

We still let Ronald's number of homework problems be $x$.

Step2: Translate Mohamad's situation to expression

Mohamad has six less than twice Ronald's amount. Twice Ronald's problems is $2x$, and six less than that is $2x-6$.

Step1: Recall Lola's and Mohamad's expressions

Lola's expression: $6x + 5$, Mohamad's expression: $2x - 6$. The product is $(6x + 5)(2x - 6)$.

Step2: Expand the product

Using the distributive property (FOIL method):
First: $6x\times2x=12x^{2}$
Outer: $6x\times(-6)=- 36x$
Inner: $5\times2x = 10x$
Last: $5\times(-6)=-30$

Step3: Combine like terms

$12x^{2}-36x + 10x-30=12x^{2}-26x - 30$

Answer:

The expression for the number of homework problems Lola has is $6x + 5$.

Sub - question 2