11. Let's call the two numbers x and y. We can set up a system of equations:
x + y = 19 (the sum of the two numbers is 19)
x - y = 55 (the difference of the two numbers is 55)
We can solve this system of equations by adding the two equations together:
(x + y) + (x - y) = 19 + 55
2x = 74
x = 37
Substituting this value back into one of the original equations, we can find the other number:
37 + y = 19
y = 19 - 37
y = -18
So the two numbers are 37 and -18.
12. Let's call the number of almond candy bars x and the number of caramel candy bars y. We can set up a system of equations:
x + y = 225 (the total number of candy bars sold is 225)
1x + 0.75y = 187.50 (the total amount of money earned is $187.50)
We can solve this system of equations by substitution. Let's solve the first equation for x:
x = 225 - y
Substituting this into the second equation, we have:
1(225 - y) + 0.75y = 187.50
225 - y + 0.75y = 187.50
225 + 0.25y = 187.50
0.25y = -37.50
y = -37.50 / 0.25
y = 150
Substituting this value back into the first equation, we can find the number of almond candy bars:
x + 150 = 225
x = 225 - 150
x = 75
So Will sold 75 almond candy bars and 150 caramel candy bars.
13. Let's call the number of students x and the number of adults y. We can set up a system of equations:
x + y = 155 (the total number of people at the game is 155)
2.50x + 4y = 492.50 (the total money received is $492.50)
We can solve this system of equations by substitution. Let's solve the first equation for x:
x = 155 - y
Substituting this into the second equation, we have:
2.50(155 - y) + 4y = 492.50
387.50 - 2.50y + 4y = 492.50
1.50y = 105
y = 105 / 1.50
y = 70
Substituting this value back into the first equation, we can find the number of students:
x + 70 = 155
x = 155 - 70
x = 85
So 85 students and 70 adults attended the game.
14. Let's call the number of nickels x and the number of dimes y. We can set up a system of equations:
x + y = 27 (the total number of coins is 27)
0.05x + 0.10y = 0.75 (the total amount of money is $0.75)
We can solve this system of equations by substitution. Let's solve the first equation for x:
x = 27 - y
Substituting this into the second equation, we have:
0.05(27 - y) + 0.10y = 0.75
1.35 - 0.05y + 0.10y = 0.75
0.05y = -0.60
y = -0.60 / 0.05
y = -12
Substituting this value back into the first equation, we can find the number of nickels:
x + (-12) = 27
x = 27 + 12
x = 39
Since it doesn't make sense to have a negative number of coins, we can conclude that there was an error in the problem statement or calculation.
11. The sum of two numbers is 19, and their difference is 55. What are the two
numbers?
12. For the fundraiser, Will sold 225 candy bars. He earns $1 for each almond candy
bar he sells and $0.75 for each caramel candy bar he sells. If he earned a total of
$187.50, how many of each type of candy bar did he sell for the fundraiser?
13. There were 155 people at the basketball game. Tickets for the game are $2.50 for
students and $4 for adults. If the total money received for admission was
$492.50, how many students and adults attended the game?
14. Jocelyn has $0.75 in her pocket made up of 27 nickels and dimes. How many of
each type of coin does she have?
1 answer
1 answer