Susan has some $2-coins and $5-coins. If there are 18 coins and the total amount of these coins is not less than $75, find the minimum number of $5-coins.
Let x = 2$ coins
Let y = 5$ coins
First equation is for the total amount of coins:
x + y = 18
Second Equation is for total amount in dollars in total from the coins:
2x + 5y = $75
Lets isolate for y
x = 18 - y
Sub into second equation
2(18 - y) + 5y = 75
36 - 2y + 5y = 75
3y = 39
y = 13
Therefore, you must have at least 13 $5 coins.
To find the minimum number of $5-coins, we can set up a system of equations based on the given information.
Let's say Susan has x $2-coins and y $5-coins.
We know that the total number of coins is 18, so we can write the equation:
x + y = 18 ...(Equation 1)
We also know that the total amount of these coins is not less than $75, so the equation becomes:
2x + 5y ≥ 75 ...(Equation 2)
Our goal is to find the minimum number of $5-coins, which is represented by 'y'.
To solve this system of equations, we can use a method called substitution:
1. Solve Equation 1 for x: x = 18 - y
2. Substitute x in Equation 2: 2(18 - y) + 5y ≥ 75
Simplify: 36 - 2y + 5y ≥ 75
36 + 3y ≥ 75
3y ≥ 75 - 36
3y ≥ 39
y ≥ 13
Therefore, the minimum number of $5-coins, y, is 13.