Question

Dylan has a bank that sorts coins as they are dropped into it. A panel on the front displays the total number of coins inside as well as the total value of these coins. The panel shows 90 coins with a value of $17.55 inside of the bank. If Dylan only collects dimes and quarters, write a system of equations in two variables or an equation in one variable that could be used to model this situation. Using your equation or system of equations, algebraically determine the number of quarters Dylan has in his bank. Dylan's mom told him that

she would replace each one of his dimes with a quarter. If he uses all of his coins, determine if Dylan would then have enough money to buy a
game priced at $20.98 if he must also pay an 8% sales tax. Justify your answer.​

Answer 1

Dylan will not have enough money. He needs $22.65 but only has $22.50

Explanation:

If Dylan's mom replaces each dime with a quarter, then Dylan will have 90 quarters.

1 Quarter = $0.25

90 x .25 = $22.50

The game costs $20.98 plus 8% sales tax

So 20.98 x .08 = $1.6784

20.98 + 1.6784 = $22.65

Dylan will not have enough money because he only has $22.50 when he needs $22.65