Tanya had $1.19 in coins none of the coins were dollars or 50-cents pieces.Josie asked Tanya for change for a dollar, but she did not have the correct chang.Which coins did Tanya have?
3x25
4x10
4x1
3 quarters 4 dimes and 4 penny
To determine which coins Tanya had, we need to consider the available coins and the given amount. Tanya had $1.19 in coins, none of which were dollars or 50-cent pieces.
Let's start by assuming Tanya had x quarters. Since Tanya didn't have any dollars or 50-cent pieces, the total value of quarters should be less than or equal to $1.19. Therefore, we can write the inequality:
0.25x ≤ 1.19
Now, we need to find the maximum value of x that satisfies this inequality. We can divide both sides of the inequality by 0.25 to isolate x:
x ≤ 1.19 / 0.25
x ≤ 4.76
This means Tanya had at most 4 quarters.
Next, let's assume Tanya had y dimes. Since she didn't have any dollars or 50-cent pieces, the total value of dimes should be less than or equal to the remaining amount after subtracting the value of quarters from $1.19. We can write the inequality:
0.10y ≤ 1.19 - (0.25 * 4)
0.10y ≤ 1.19 - 1.00
0.10y ≤ 0.19
Dividing both sides of the inequality by 0.10:
y ≤ 0.19 / 0.10
y ≤ 1.90
This means Tanya had at most 1 dime.
Finally, let's assume Tanya had z nickels. Again, since she didn't have any dollars or 50-cent pieces, the total value of nickels should be less than or equal to the remaining amount after subtracting the value of quarters and dimes from $1.19. We can write the inequality:
0.05z ≤ 1.19 - (0.25 * 4) - (0.10 * 1)
0.05z ≤ 1.19 - 1.00 - 0.10
0.05z ≤ 0.09
Dividing both sides of the inequality by 0.05:
z ≤ 0.09 / 0.05
z ≤ 1.80
This means Tanya had at most 1 nickel.
In summary, Tanya could have had at most 4 quarters, 1 dime, and 1 nickel.