A string is cut in two so that one section is 5 inches longer than the other. Twice the length of the longer section is three times the length of the shorter section. Write an equation that allows you to solve for the length of the shorter section. How long is the shorter section?(1 point)
Let x be the length of the shorter section of the string.
The longer section is 5 inches longer, so its length is x + 5.
Twice the length of the longer section is three times the length of the shorter section:
2(x + 5) = 3x
2x + 10 = 3x
10 = 3x - 2x
10 = x
Therefore, the length of the shorter section is 10 inches. Answer: \boxed{10}.
Andrea is 6 years younger than Tony. In two years, Tony will be three times as old as Andrea. Let a be Tony’s current age. Which of these linear equations can be used to find Andrea’s and Tony’s current ages?(1 point)
Let x be the current age of Andrea.
Since Andrea is 6 years younger than Tony, Tony's current age is x + 6.
In two years, Tony will be x + 6 + 2 = x + 8 years old, and Andrea will be x + 2 years old.
In two years, Tony will be three times as old as Andrea:
x + 8 = 3(x + 2)
x + 8 = 3x + 6
8 - 6 = 3x - x
2 = 2x
Therefore, the equation that can be used to find Andrea's and Tony's current ages is 2 = 2x.
Linear Equations in Real-World Scenarios Quick Check
2 of 52 of 5 Items
Question
Andrea is 6 years younger than Tony. In two years, Tony will be three times as old as Andrea. Let a be Tony’s current age. Which of these linear equations can be used to find Andrea’s and Tony’s current ages?(1 point)
Responses
a+2=3(a+6+2)
a plus 2 equals 3 left parenthesis a plus 6 plus 2 right parenthesis
3(a+2)=a−6+2
3 left parenthesis a plus 2 right parenthesis equals a minus 6 plus 2
a+2=3(a−6+2)
a plus 2 equals 3 left parenthesis a minus 6 plus 2 right parenthesis
a=3(a+2)
None of the given equations can be used to find Andrea's and Tony's current ages.
Option a+2=3(a+6+2) is incorrect because it incorrectly adds an extra 6 to Andrea's age.
Option 3(a+2)=a−6+2 is incorrect because it incorrectly subtracts 6 from Tony's age.
Option a+2=3(a−6+2) is incorrect because it incorrectly subtracts 6 from Tony's age.
Option a=3(a+2) is incorrect because it incorrectly multiplies Andrea's age by 3.
Five less than three-fourths of x is seven. If x equals 16, what is the last property of equality you would use to justify the solution to this problem?
Division Property of Equality
Addition Property of Equality
Identity Property of Multiplication
Subtraction Property of Equality
To solve this problem, we can break it down step by step:
1. Let's assume the length of the shorter section as "x" inches.
2. According to the problem, the longer section is 5 inches longer than the shorter section. So, the length of the longer section would be x + 5 inches.
3. Twice the length of the longer section is three times the length of the shorter section. In equation form, this can be written as:
2 * (x + 5) = 3 * x
4. Now, let's solve the equation to find the value of x, which represents the length of the shorter section.
Distribute the 2 on the left side of the equation:
2x + 10 = 3x
Subtract 2x from both sides to isolate the x term:
10 = 3x - 2x
Simplify:
10 = x
So, the length of the shorter section is 10 inches.