Julius has three times as many stamps in his collection as his friends Liam and Mario combined. Liam has 10 stamps in his collection. Julius has 87 stamps in his collection. How many stamps does Mario have in his collection?
The equation 3(x + 10) = 87 models this situation. Which choice shows the sequence of operations needed to solve this problem, using both arithmetic and algebra?
1. 3x + 30 = 87
2. 87 - 30 = 57
3. 57 รท 3 = 19
4. x = 19
To solve this problem using the equation 3(x + 10) = 87, you can follow these steps:
1. Start by distributing the 3 to the terms inside the parentheses: 3x + 30 = 87.
2. Next, subtract 30 from both sides to isolate the variable: 3x = 57.
3. Then, divide both sides of the equation by 3 to solve for x: x = 19.
After finding the value of x as 19, you can conclude that Mario has 19 stamps in his collection.
To solve this problem, we can follow these steps:
1. Start with the equation: 3(x + 10) = 87.
2. Distribute the 3 to the terms inside the parentheses: 3x + 30 = 87.
3. Subtract 30 from both sides of the equation: 3x = 87 - 30.
4. Simplify the right side of the equation: 3x = 57.
5. Divide both sides of the equation by 3 to solve for x: x = 57/3.
6. Simplify the right side of the equation: x = 19.
Therefore, Mario has 19 stamps in his collection.