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Contributor: Ashley Nail Murphy. Lesson ID: 14182
Ready for an adventure? Every adventure needs snacks! Use multi-step equations with fractional coefficients to help you sharpen your problem-solving skills...and make snacks!
Alex and Jade are getting ready for a camping adventure and decide to mix up a big bowl of trail mix for a snack.
Alex brought raisins, and Jade brought peanuts. They combine the ingredients in a large bowl and stir them up!
Alex adds 4 cups of raisins to the mix. Jade brought a lot of peanuts, so they decided only to use 2/3 of her peanuts.
After mixing, they end up with 10 cups of trail mix.
Now, here’s the challenge.
To solve this, Alex's dad writes an equation.
| 2 | p | + | 4 | = | 10 | |
| 3 |
In this equation, p stands for the amount of peanuts Jade brought.
The friends used 2/3 p cups of Jade’s peanuts plus 4 cups of Alex’s raisins to make 10 cups of trail mix in total.
Use what you know about fractions and solving equations to help the campers!
Look at the equation.
| 2 | p | + | 4 | = | 10 | |
| 3 |
Look at the parts of this equation.
p is a variable. A variable is a symbol for an unknown value. You need to find the value of p in this equation — the number of peanuts Jade brought.
2/3 is the coefficient. A coefficient is a number that is multiplied by the variable. This number is always right before the variable.
| So, | 2 | p | means | 2 | x | p. | |
| 3 | 3 |
Now that you understand the important parts of this equation, you can start to solve it!
Step 1: Isolate p
First, you need to get rid of the + 4 so that you can focus on p.
Since it says + 4, do the opposite. Subtract 4 from both sides of the equation.
This step brings you one step closer to isolating p.
Look closer at the first step.
| 2 | p | + | 4 | - | 4 | = | 10 | - | 4 | |
| 3 |
| 2 | p | = | 6 | |||
| 3 |
Step 2: Remove the Coefficient
Now, you are ready to isolate the p by getting rid of 2/3.
Remember, since 2/3 is a coefficient, you are multiplying it by p. To reverse that, do the opposite operation, which is division.
| 2 | p | ÷ | 2 | = | 6 | ÷ | 2 | |
| 3 | 3 | 3 |
This is where it gets tricky! In order to divide fractions, you need to multiply using a reciprocal. A reciprocal is when you flip a fraction.
| So, | 2 | becomes | 3 | . | ||
| 3 | 2 |
Remember this phrase: Keep. Change. Flip. Keep the first number, change the division to multiplication, and flip the second fraction.
Apply this to both sides of the equation.
| So, | 2 | p | ÷ | 2 | = | 6 | ÷ | 2 | becomes | 2 | p | x | 3 | = | 6 | x | 3 | |
| 3 | 3 | 1 | 3 | 3 | 2 | 1 | 2 |
| 2 | p | x | 3 | = | 0 | p | |
| 3 | 2 |
| 6 | x | 3 | = | 18 | |
| 1 | 2 | 2 |
Step 3: Solve and Simplify
Now, p is alone, and you solved the equation! All you have to do is simplify.
| p | = | 18 | = | 18 | ÷ | 2 | = | 9 | |
| 2 |
p = 9
p was the unknown amount of peanuts Jade brought camping. Jade had 9 cups of peanuts before they made trail mix! That was a lot of peanuts!
Check out the images below to review the steps to solve this equation in order.
This skill not only helps you solve equations but also builds your problem-solving abilities, preparing you for future mathematical adventures.
Visit the Got It? section to practice!
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