Q58. - Algebra 2

Question

For exercise 56-58, use the following information.

Ian has $6.00, and he wants to buy paper for his scrapbook. A sheet of printed paper costs 30¢, and a sheet of solid color paper costs 15¢.

 

Does Ian have enough money to buy 14 pieces of each type of paper?

Step-by-Step Solution

Answer

Ian does not have enough money to buy 14 pieces of each type of paper.

Step 1 - Convert cents to dollar

 1 dollar is equal to 100 cents, therefore, 30¢ will be equal to 0.3$ and similarly, 15¢ will be equal to 0.15$.

Step 2 - Define the variables

Let Ian buy ‘x’ sheets of printed paper and ‘y’ sheets of solid color paper.

Since, 1 sheet of printed paper costs 0.3$, therefore, ‘x’ sheets of printed paper will cost $0.3x$  and similarly, since 1 sheet of solid color paper costs 0.15$, therefore, ‘y’ sheets of solid color paper will cost $0.15y$.

Step 3 - Write the equation

Note that Ian can buy the sheets worth 6$ or less than 6$, but not more than that. Therefore, the inequality will be:  $0.3x+0.15y\le 6$.

Step 4 - State the conclusion

Substitute 14 for x and 14 for y into the inequality $0.3x+0.15y\le 6$.

$\begin{array}{c}0.3\left(14\right)+0.15\left(14\right)\le 6\\ 4.2+2.1\le 6\\ 6.3\le 6\text{ False}\end{array}$

Therefore, Ian does not have enough money to buy 14 pieces of each type of paper.