Carmen had an end-of-the-year celebration for her employees. It cost her seven dollars per employee for food and one dollar per employee for an end-of-the-year souvenir. If 12 employees attended the party, use the distributive property to find the total cost.
If we let 𝑥 stand for the number of employees and it cost seven dollars per employee for food, that would be seven times 𝑥 and so plus one dollar per employee for an end-of-the-year souvenir, so one times 𝑥. So 𝑥 is being multiplied to both of these. Therefore, we could rewrite it as 𝑥 times seven plus one. However, seven plus one does reduce to be eight. So it’s actually equal to eight 𝑥.
We could use the distributive property to find the total cost two different ways actually: we could take seven times 12 plus one times 12 or we could just take eight times 12. Seven times 12 is 84 and one times 12 is 12. 84 plus 12 equals 96 or we could have done eight times 12, which is also 96. Therefore, the total cost would be 96 dollars.