Will the given equation solve the problem? Choose all which will.
Responses
A Problem: The sum of twice a number and −6 is 9 more than the opposite of the number. Find the number. Equation: 2n − 6 = 9 − nProblem: The sum of twice a number and −6 is 9 more than the opposite of the number. Find the number. Equation: 2n − 6 = 9 − n
B Problem: Anna drove 450 km in 6 hours. Find her rate of travel. Equation: 450r = 6Problem: Anna drove 450 km in 6 hours. Find her rate of travel. Equation: 450r = 6
C Problem: Three times a number increased by 44 is the same as the opposite of the number. Find the number. Equation: 3n + 44 = −nProblem: Three times a number increased by 44 is the same as the opposite of the number. Find the number. Equation: 3n + 44 = −n
D Problem: Sara collects her change and realizes that she has five times as many dimes as quarters. The total amount for the change is $5.25. Find the number of quarters in her collection. Equation: x + 10x = $5.25Problem: Sara collects her change and realizes that she has five times as many dimes as quarters. The total amount for the change is $5.25. Find the number of quarters in her collection. Equation: x + 10x = $5.25
A, B, C, and D are all equations that can solve their respective problems.
The equations that will solve the given problems are:
A) Problem: The sum of twice a number and −6 is 9 more than the opposite of the number. Find the number. Equation: 2n − 6 = 9 − n
C) Problem: Three times a number increased by 44 is the same as the opposite of the number. Find the number. Equation: 3n + 44 = −n
D) Problem: Sara collects her change and realizes that she has five times as many dimes as quarters. The total amount for the change is $5.25. Find the number of quarters in her collection. Equation: x + 10x = $5.25
To determine which equation(s) will solve the given problem, let's analyze each equation and see if it matches the problem description.
A) Problem: The sum of twice a number and −6 is 9 more than the opposite of the number. Find the number.
Equation: 2n − 6 = 9 − n
This equation matches the problem description. It represents the sum of twice a number (2n) and -6 on the left side, and 9 more than the opposite of the number (9 - n) on the right side. Therefore, this equation will solve the problem.
B) Problem: Anna drove 450 km in 6 hours. Find her rate of travel.
Equation: 450r = 6
This equation does not match the problem description. It represents the distance (450 km) multiplied by the rate of travel (r) on the left side, and the time (6) on the right side. It does not solve the problem of finding Anna's rate of travel. Therefore, this equation will not solve the problem.
C) Problem: Three times a number increased by 44 is the same as the opposite of the number. Find the number.
Equation: 3n + 44 = −n
This equation matches the problem description. It represents three times a number (3n) increased by 44 on the left side, and the opposite of the number (-n) on the right side. Therefore, this equation will solve the problem.
D) Problem: Sara collects her change and realizes that she has five times as many dimes as quarters. The total amount for the change is $5.25. Find the number of quarters in her collection.
Equation: x + 10x = $5.25
This equation does not match the problem description. It represents the number of quarters (x) added to ten times that number of dimes (10x) on the left side, and the total amount of change ($5.25) on the right side. It does not solve the problem of finding the number of quarters. Therefore, this equation will not solve the problem.
Therefore, the equations that will solve the given problems are A and C.