Kareem has a collection of dimes and quarters. He can tell that he has more quarters than dimes and he knows he has at most $2. Could Kareem have 4 dimes and 7 quarters? EXPLAIN why or why not.
MATH

Kareem could NOT have 4 dimes and 7 quarters

Step-by-step explanation:

Inequalities

Kareem's collection of coins includes dimes and quarters. He has more quarters than dimes and he has at most $2. Recall each dime is worth $0.10 and each quarter is worth $0.25.

If d is the number of dimes and q is the number of quarters, both conditions can be written as:

q > d

0.10d + 0.25q ≤ 2

We're required to find out if Kareem could have d=4 and q=7. Substituting in both inequalities:

7 > 4 (true)

0.10*4 + 0.25*7 ≤ 2

0.4 + 1.75 ≤ 2

2.15 ≤ 2  (false)

It's noted the first inequality is satisfied, but not the second, thus

Kareem could NOT have 4 dimes and 7 quarters