Question

martin collects 20 cent and 50 cents coins. He has 37 coins, and the total value of the coins is 11.30.How many coins of each type does Martin have?

Answer 1

Martin has 24 twenty cent coins and 13 fifty cent coins. We found this by setting up a system of equations based on the total number of coins and their combined value.

Step-by-step explanation:

Martin collects 20 cent and 50 cent coins. He has 37 coins in total, and their combined value is $11.30. To determine how many of each type of coin he has, we can set up a system of equations.

Let x be the number of 20 cent coins and y be the number of 50 cent coins. We then have:

• x + y = 37 (since there are 37 coins in total)
• 0.20x + 0.50y = 11.30 (since the total value of the coins is $11.30)

Solving this system of equations, we first multiply the second equation by 10 to eliminate decimals:

• 2x + 5y = 113

Then we can multiply the first equation by 2 and subtract it from the modified second equation to eliminate x:

• (2x + 5y) - (2x + 2y) = 113 - 74
• 3y = 39
• y = 13

Substituting y = 13 into the first equation, we get:

• x + 13 = 37
• x = 24

So Martin has 24 twenty cent coins and 13 fifty cent coins.