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Erik’s Floor. By: Grant Wiler www.hsiehzam.com/systems-of-equations/Eriks-Floor. Step 1: Making your Equations. Using the story below, we will make our equations to solve with.
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Erik’s Floor By: Grant Wiler www.hsiehzam.com/systems-of-equations/Eriks-Floor
Step 1: Making your Equations • Using the story below, we will make our equations to solve with. • Story: A flood has wrecked the town of Donkeymonkers, and, more importantly, Erik’s floor. To replace it, he will need 250 tiles, some black, some white. He needs 50 more black tiles than white tiles so he can fix his wall as well. Black tiles cost 2$, white tiles 3$, and he has a 600$ budget.
Now to make your Equations • Equation 1: The first equation will be based off the cost of the tiles. For this equation, black tiles are x and white tiles y. Now, since black tiles are 2 dollars and white tiles are three dollars, you should get this equation: • 2x+3y=600$ • Equation 2: Now, since he needs 250 tiles, using the same x and y variables, your next equation should be • x+y=250 • Equation 3: Now, we will make one more equation based off the difference between the variable. Since x is 50 more than y, our last equation should be • y=x-50
Now to make your Equations • Equation 1: The first equation will be based off the cost of the tiles. For this equation, black tiles are x and white tiles y. Now, since black tiles are 2 dollars and white tiles are three dollars, you should get this equation: • 2x+3y=600$ • Equation 2: Now, since he needs 250 tiles, using the same x and y variables, your next equation should be • x+y=250 • Equation 3: Now, we will make one more equation based off the difference between the variable. Since x is 50 more than y, our last equation should be • y=x-50
Now to solve the Equations • 1st, use substitution 2x+3y=600 y=x-50 Substitute x-50 for y. 2x+3(x-50)=600 Distribute 2x+3x-150=600 Merge the x 5x-150=600 Solve 5x-150=600 5x= 750 +150 +150 5 x=150 0 750
Now to solve the Equations • 1st, use substitution 2x+3y=600 y=x-50 Substitute x-50 for y. 2x+3(x-50)=600 Distribute 2x+3x-150=600 Merge the x 5x-150=600 Solve 5x-150=600 5x= 750 +150 +150 5 x=150 0 750
Now to solve the Equations • 1st, use substitution 2x+3y=600 y=x-50 Substitute x-50 for y. 2x+3(x-50)=600 Distribute 2x+3x-150=600 Merge the x 5x-150=600 Solve 5x-150=600 5x= 750 +150 +150 5 x=150 0 750
Now to solve the Equations • 1st, use substitution 2x+3y=600 y=x-50 Substitute x-50 for y. 2x+3(x-50)=600 Distribute 2x+3x-150=600 Merge the x 5x-150=600 Solve 5x-150=600 5x= 750 +150 +150 5 x=150 0 750
Now to solve the Equations • 1st, use substitution 2x+3y=600 y=x-50 Substitute x-50 for y. 2x+3(x-50)=600 Distribute 2x+3x-150=600 Merge the x 5x-150=600 Solve 5x-150=600 5x= 750 +150 +150 5 x=150 0 750
Now to solve the Equations • 1st, use substitution 2x+3y=600 y=x-50 Substitute x-50 for y. 2x+3(x-50)=600 Distribute 2x+3x-150=600 Merge the x 5x-150=600 Solve 5x-150=600 5x= 750 +150 +150 5 x=150 0 750
Now to solve the Equations • 1st, use substitution 2x+3y=600 y=x-50 Substitute x-50 for y. 2x+3(x-50)=600 Now, using X you can find y, Distribute Y=100 2x+3x-150=600 Merge the x 5x-150=600 Solve 5x-150=600 5x= 750 +150 +150 5 x=150 0 750
Checking your work • Now that you’ve solved this equation, the time has come to check your work. Now, to check it, you must solve the equation in a different way. For this demonstration, we’ll be using elimination.
Solving With Elimination • The Equations: 2x+3y=600 x+y= 250 • Start with: • 2x+3y=600 • x+y=250 we already know the answer, so we’ll just plug in our answers. 3x= 450/3 is 150 2y=200/2 is 100.
