Daniel D. answered • 02/07/19
How can I help?
This question is a system of linear equations. There are sentences that translate into algebraic equations. Let's see what is known.
How ever many quarters and dimes Jamal has total 70 coins. The value of a quarter is $0.25, the value of a dime is $0.10, and the total value of all of the coins is $13.30.
Using Q for quarters and D for dimes, we can now write two equations to help us solve. The first equation is for quantity and the second will be for value.
Q + D = 70.
Next, the value of each coin will be placed in front of the variables.
0.25Q + 0.10D = 13.30
This system may not be so fun to graph or use substitution. That leaves only elimination in order to solve. In order to perform elimination, some variable when added or subtracted must equal 0. If that isn't possible then multiplication must occur first by choosing any variable you wish to eliminate first. I will eliminate the dimes by first distributing ten cents through the first equation.
0.10(Q + D = 70)
0.10*Q + 0.10*D = 0.10*70
0.10Q + 0.10D = 7
0.10Q + 0.10D = 7
0.25Q + 0.10D = 13.30
The coefficient for dimes have the same sign. This means that subtraction is required in order to eliminate. By subtracting each column vertically, there is now:
(0.10Q-0.25Q) + (0.10D-0.10D) = (7-13.30)
-0.15Q = -6.30
Divide both sides by -0.15 to find:
Q = 42
Plug 42 into the first equation for Q.
42 + D = 70.
Subtract 42 from both sides to find D.
D = 28
Now, the second equation can prove it.
0.25(42) + 0.10(28) = 13.30
10.50 + 2.80 = 13.30
13.30 = 13.30
We have a true statement so we know that we have the correct solution.
