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}.
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)
6 answers
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.
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)
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.
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
Division Property of Equality
Addition Property of Equality
Identity Property of Multiplication
Subtraction Property of Equality
1 answer