Question

Matthew has n nickels and d dimes. He has a minimum of $1 worth of coins

Answer 1

Answer:  $5n + 10d \ge 100$

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Explanation:

5n represents the value of all the nickels, where n is the number of nickels. Let's say he had 8 nickels. This would mean 5n = 5*8 = 40 cents is from just the nickels.

The 10d represents the value of all the dimes. For example, if he had d = 2 dimes, then he has 20 cents from those dimes because 10d = 10*2 = 20.

Combining the two expressions leads to 5n+10d as the total value of both types of coins. This total value is in cents. We want this value to be 100 cents or more. This is why we set 5n+10d to be greater than or equal to 100. That's how we arrive to $5n+10d \ge 100$

Optionally we can divide each term by 5 to get $n + 2d \ge 20$ ,but I'll put the other inequality as the answer because it seems more descriptive in my opinion. Keeping 5n shows each nickel is 5 cents, and 10d shows each dime is 10 cents. Something like n+2d loses a bit of its descriptive nature.