Katie W. answered • 06/10/15
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We have two unknown variables in this equation: pennies (P) and quarters (Q)
Next, we are given two numbers: 15 which tells us how many coins and $2.79 which tells us the total amount we have. So these are two different equations.
So we start with the first number: 15. This tells us the number of coins we have. We already know our two unknowns: pennies (P) and quarters (Q). So we ask "How would we come up with an equation using pennies and quarters that tell us how many coins we have?" We find this by counting how many of each coin we have; or by taking the amount of pennies we have and adding it to the number of quarters we have:
Q + P = 15
Now we need a second equation (the reason we need two equations is because we have two unknown variables we are trying to solve for; this is generally an indicator of how many equations you will need. If there are three unknowns, you would have to come up with three equations, etc). So we look at the second number they gave us: $2.79. Since this is a dollar amount, this should be an indicator that you will need to dollar amount of the coins included in your equation as well. We know that pennies = 0.01 and quarters = 0.25. To come up with how much you have in dollar amount for each coin, you multiply the number of coins you have with how much it's worth. For example, if we had one quarter, that equals 0.25. If we have two quarters, that equals 0.50. To make an equation for this you just take 0.25 * the total quarters you have, which is this case is 2. So 2 * 0.25 = 0.5.
Quarters = 0.25 x Q
Pennies = 0.01 x P
To make this equation, you would just need to add the dollar amount you have of each coin to get the total:
0.25Q + 0.01P = 2.79
We now have two equations with two unknowns. You can solve this by graphing, substitution method, or elimination method.
Q + P = 15
0.25Q + 0.01P = 2.79
Please let me know if you need further help from this step.
C R.
06/10/15