Eduardo and Sarawong are selling wrapping paper for a school fundraiser. Eduardo sold 5 rolls of plain wrapping paper and 5 rolls of holiday wrapping paper for a total of $185. Sarawong sold 14 rolls of plain and 5 rolls of holiday for a total of $338. Find the cost per roll of plain wrapping paper and 5 rolls of holiday wrapping paper.

Answer: A roll of plain wrapping paper costs $17, while a roll of holiday wrapping paper costs $20.

Step-by-step explanation: First let us represent a roll of plain wrapping paper with letter p and a roll of holiday wrapping paper would be represented by d. If Eduardo sold 5 rolls of plain wrapping paper and 5 rolls of holiday wrapping paper for $185, then we can express this as

5p + 5d = 185

Also if Sarawong sold 14 rolls of plain wrapping paper and 5 rolls of holiday wrapping paper for $338, then this too can be expressed as

14p + 5d = 338

Now we have a pair of simultaneous equations which are,

5p + 5d = 185 - - - (1)

14p + 5d = 338 - - - (2)

Since all the variables have coefficients greater than 1, we shall use the elimination method. Note that the coefficients of the d variable are both 5, so straight away we subtract equation (1) from equation (2) and we now have;

(14p - 5p) + (5d - 5d) = 338 - 185

9p = 153

Divide both sides of the equation by 9

p = 17

Having calculated p, we can now substitute for the value of p into equation (1)

5p + 5d = 185

5 (17) + 5d = 185

85 + 5d = 185

Subtract 85 from both sides of the equation

5d = 100

Divide both sides of the equation by 5

d = 20

Hence, the cost per roll of plain wrapping paper is $17, while the cost per roll of holiday wrapping paper is $20.