Transcript Solving Equations: Word Problems
We're at the secret hideout of Dr. Evil, located on Volcano Island. He needs some gold to buy a present for his mommy's birthday.
Mommy Evil likes bling, so she wants a ring with as many diamonds as possible. Every jewel on the ring cost a measely 10 gold bars (obviously the typical currency for villans). But the problem is: he's a bit short on gold.
Word Problem Example
To determine how much of his stuff he needs to sell, we should convert the information from the word problem into an equation.
First, he lists one of his private islands on Evil-Bay and his asking price is 50 gold bars - quite a bargain!
Next, he'll sell 20 of his most evil robotic rocket crocs for 5 gold bars each. Hopefully they sell quickly. There's not much time until Mommy Evil's birthday.
He wonders how much bling he can put on the ring if each diamond costs 10 gold bars each. Let the number of diamonds equal x.
Translating the Word Problem and Writing the Equation
Let's write an equation. On the left side of the equal sign, write the price of his private island times the number of islands, 50 times 1, and add the price times the number of rocket crocs he plans to sell, 5 times 20.
On the right side, write the cost in gold bars, 10, times the unknown amount, x, which stands for the total number of diamonds he can put on his mom's ring.
Solving the Word Problem Example 1
Now, to solve the equation for x, you have to simplify the equation using PEMDAS and opposite operations.
- Here, multiplication is first. 50 · 1 = 50 and 5 · 20 = 100.
- Now we have to add: 50 + 100 = 150.
- 150 = 10x. To isolate x, we use the opposite operation here. We divide both sides by 10.
- x = 15. The ring for Mommy could have 15 diamonds.
Solving the Word Problem Example 2
But it's Mommy's 60th birthday and Dr. Evil decides he must buy her a ring with 60 diamonds. Wow! In addition to the island, how many rocket crocs will he need to sell? Let this now be x.
Now let's write another equation. Again, write the price of the island multiplied by the number of islands for sale and add the price of the rocket crocs times x on the left side of the equation.
Make this equal to the price of the gold bars times the number of diamonds Dr. Evil wishes to put on his mom's ring. Simplify the equation using PEMDAS and solve for the unknown variable using opposite operations.
- Again we start with multiplication here: 50 · 1 = 50 and 10 · 60 = 600.
- Now let's get rid of the 50 to isolate x. We subtract 50 on both sides. So 5x = 550.
- Now isolate x by dividing both sides by 5.
- x = 110. Dr. Evil will need to sell 110 rocket crocs.
Solving the Word Problem Example 3
What? You've gotta be kidding! He has only 55 of the rockets crocs! Oh boy, what can he do? Eureka! Dr. Evil realizes he can raise the price of the rocket crocs. Back to the equation...
This time, the unknown number, 'x' is the new price of the rocket crocs. So, again, write the price of the island multiplied by the number of islands for sale and add the price of the rocket crocs, our new x, times 55, the number of rocket crocs he has, on the left side of the equation.
Set this equal to the value and the number of diamonds on the ring. Simplify and solve.
- Multiplication first: 50 · 1 = 50, x · 55 = 55x, 10 · 60 = 600.
- Now to get rid of this 50, we use opposite operations by subtracting 50 from both sides. So 55x = 550.
- To isolate x here we divide both sides by 55.
- x = 10. This means he must sell the rocket crocs for 10 gold bars each.
Great, now that he's finished with his calculations, he can start the sale. Oh no! One of the robotic rocket crocs just exploded! Maybe Dr. Evil can buy smaller diamonds?