Sandra has eight coins witch total $0.87. what coins does she have (Hint:make a chart or a list)
Did you make the chart or list? What did you find?
10 10 10 10 10 10 10 10 5 1 1
To determine the coins Sandra has, we can create a chart or list and utilize the given information. Let's start by listing the possible coins and their respective values:
- Penny (1 cent)
- Nickel (5 cents)
- Dime (10 cents)
- Quarter (25 cents)
Now, let's create a chart and assign variables for each coin:
Coins | Quantity (variable) | Value per Coin | Total Value (Quantity * Value)
--------|--------------------|----------------|-------------------------------
Pennies | x | 0.01 | (x * 0.01)
Nickels | y | 0.05 | (y * 0.05)
Dimes | z | 0.10 | (z * 0.10)
Quarters| w | 0.25 | (w * 0.25)
Given that Sandra has a total of eight coins and the total value is $0.87, we can set up the following equation:
(x * 0.01) + (y * 0.05) + (z * 0.10) + (w * 0.25) = 0.87
Now, let's solve for the variables. Since Sandra has eight coins, we know that x + y + z + w = 8. We can rearrange this equation to express one variable in terms of the others and substitute it into the first equation:
x = 8 - y - z - w
Substituting this value of x into the equation:
(8 - y - z - w) * 0.01 + (y * 0.05) + (z * 0.10) + (w * 0.25) = 0.87
Simplifying the equation gives:
0.08 - 0.01y - 0.01z - 0.01w + 0.05y + 0.10z + 0.25w = 0.87
Now, combine like terms:
0.25w + 0.10z - 0.01z - 0.01y - 0.01w +0.05y = 0.87 - 0.08
Simplifying further:
0.24w + 0.09z + 0.04y = 0.79
Since we are dealing with whole numbers of coins, we need to determine the possible values for w, z, and y that make the left side of the equation equal to a number smaller than or equal to 0.79. By trying different combinations, we can find the answer.
Alternatively, we can use programming or calculators capable of solving equations to find integer values for w, z, and y that satisfy the equation. In this specific case, the solution is:
w = 3, z = 2, y = 3
So, Sandra has 3 quarters, 2 dimes, and 3 nickels to total $0.87 with eight coins.