how do i solve, marge has six coins that total $1.15. she cannot make change for $1.00, 1/2 dollar, a quarter, a dime, or a nickel.what coins does she have?
.50, .25, & 4 - .10s
how many coins do you need to make $1.15 cents
1.15 pennies
To solve this problem, we need to determine the types and number of coins that Marge has. Let's break it down step by step:
Step 1: Set up an equation
Let's assume Marge has x number of pennies, y number of nickels, z number of dimes, a number of quarters, b number of half dollars, and c number of dollar coins. We can set up the equation as:
0.01x + 0.05y + 0.10z + 0.25a + 0.50b + 1.00c = 1.15
Step 2: Identify the conditions
We know that Marge cannot make change for $1.00, 1/2 dollar, a quarter, a dime, or a nickel. This means that:
a ≠ 1 (Marge does not have a quarter)
b ≠ 2 (Marge does not have two half dollars)
c ≠ 1 (Marge does not have a dollar coin)
Step 3: Simplify and solve
With the given conditions, we can simplify the equation. Let's multiply both sides by 100 to eliminate the decimals:
x + 5y + 10z + 25a + 50b + 100c = 115
Now let's examine the possibilities for a, b, and c:
1) If a = 0, b can only be 0, 1, or 2 since b ≠ 2.
- If b = 0, c must be 1 since c ≠ 1.
- If b = 1, c can only be 0 or 1, but if c = 1, Marge would have a dollar coin.
- If b = 2, it contradicts the condition b ≠ 2.
2) If a = 1, b cannot be 1 or 2 since b ≠ 2.
- If b = 0, c must be 0 or 2, but if c = 1, Marge would have a dollar coin.
- If b = 2, it contradicts the condition b ≠ 2.
Therefore, there is no valid solution that satisfies the given conditions.
In conclusion, based on the given information, there are no possible coins that Marge could have.