Help! I need to get these questions done before 8:30.
Write a system of equations to model each situation. Solve my any method.
4.You and some friends buy hamburgers and milkshakes for lunch. A hamburger costs $1.50 and a milkshake costs $2.00. The total bill for 12 items is $21.50. How many hamburgers and how many milkshakes did your group buy?
5. A collection of dimes and nickels is worth $0.55 There are 7 coins in all. How many dimes and nickels are there?
I apologize for the delay.
For question 4, we can set up a system of equations as:
h + m = 12
1.5h + 2m = 21.5
where h represents the number of hamburgers and m represents the number of milkshakes.
We can solve this system using elimination method. First, multiply the first equation by -2 and add it to the second equation:
-2h - 2m = -24
1.5h + 2m = 21.5
--------------
-0.5h = -2.5
Solving for h, we get:
h = 5
Substitute h = 5 into the first equation to solve for m:
5 + m = 12
m = 7
Therefore, the group bought 5 hamburgers and 7 milkshakes.
For question 5, we can set up a system of equations as:
d + n = 7
0.1d + 0.05n = 0.55
where d represents the number of dimes and n represents the number of nickels.
We can solve this system using substitution method. Solve the first equation for n:
n = 7 - d
Substitute n = 7 - d into the second equation:
0.1d + 0.05(7-d) = 0.55
0.1d + 0.35 - 0.05d = 0.55
0.05d = 0.2
d = 4
Substitute d = 4 into the first equation to solve for n:
4 + n = 7
n = 3
Therefore, there are 4 dimes and 3 nickels.
i dont know how to do them
Be patient. A math tutor will come on line sooner or later and may be able to help you. Ms. Sue and I can't.
h + m = 12 ----> m = 12=h
1.5h + 2m = 21.50
or 3h + 4m = 43
I would solve these by substitution.
coin problem:
d+n = 7 **
10d + 5n = 55
divide by 5
2d + n = 11 ***
subtract ** from *** , and it comes apart very nicely
so no-ones gonna answer then?
ok
Sure! Let's work on each question one by one.
Question 4:
To model the situation, we need to define variables for the number of hamburgers and milkshakes. Let's say:
x = number of hamburgers
y = number of milkshakes
The cost of a hamburger is $1.50, so the total cost of hamburgers can be expressed as 1.50x. Similarly, the cost of a milkshake is $2.00, so the total cost of milkshakes can be expressed as 2.00y.
The total bill for 12 items is $21.50, so we can set up the equation:
1.50x + 2.00y = 21.50
Now, to solve this system of equations.
Method 1: Substitution
- Solve one equation for one variable and substitute that expression into the other equation.
- Let's solve the first equation for x:
x = (21.50 - 2.00y) / 1.50
- Substitute this expression for x in the second equation:
1.50((21.50 - 2.00y) / 1.50) + 2.00y = 21.50
- Simplify and solve for y:
(21.50 - 2.00y) + 2.00y = 21.50
21.50 - 2.00y + 2.00y = 21.50
21.50 = 21.50
This equation implies that y can be any value. Since we cannot determine a specific value for y, let's use the equation we derived for x instead:
x = (21.50 - 2.00y) / 1.50
Now, we have an equation that relates x and y. To find specific values for x and y, we need additional information or constraints.
Method 2: Elimination
- Multiply one equation by a constant such that when added or subtracted to the other equation, one variable can be eliminated.
- In this case, we can multiply the first equation by 2 to make the coefficients of y equal:
3.00x + 4.00y = 43.00
- Subtract the second equation from the modified first equation:
(3.00x + 4.00y) - (3.00x + 2.00y) = 43.00 - 21.50
2.00y = 21.50
y = 10.75
- Substitute the value of y into one of the original equations to find x:
1.50x + 2.00(10.75) = 21.50
1.50x + 21.50 = 21.50
1.50x = 0
x = 0
Based on these calculations, the number of hamburgers (x) would be 0 and the number of milkshakes (y) would be 10.75. However, it is not realistic to have a fractional number of milkshakes, so we need to reevaluate our approach.
It seems that there might be an error or missing information in the problem. Please double-check the problem and the given information.
Now let's move on to question 5.
Question 5:
Similarly, we need to define variables for the number of dimes and nickels. Let's say:
x = number of dimes
y = number of nickels
The value of a dime is $0.10, so the total value of dimes can be expressed as 0.10x. Similarly, the value of a nickel is $0.05, so the total value of nickels can be expressed as 0.05y.
The total value of all coins is $0.55, so we can set up the equation:
0.10x + 0.05y = 0.55
Now, let's solve this system of equations.
Method 1: Substitution
- Solve one equation for one variable and substitute that expression into the other equation.
- Let's solve the first equation for x:
x = (0.55 - 0.05y) / 0.10
- Substitute this expression for x in the second equation:
0.10((0.55 - 0.05y) / 0.10) + 0.05y = 0.55
- Simplify and solve for y:
(0.55 - 0.05y) + 0.05y = 0.55
0.55 - 0.05y + 0.05y = 0.55
0.55 = 0.55
This equation implies that y can be any value. Since we cannot determine a specific value for y, let's use the equation we derived for x instead:
x = (0.55 - 0.05y) / 0.10
Now, we have an equation that relates x and y. To find specific values for x and y, we need additional information or constraints.
Method 2: Elimination
- Multiply one equation by a constant such that when added or subtracted to the other equation, one variable can be eliminated.
- In this case, we can multiply the first equation by 2 to make the coefficients of y equal:
0.20x + 0.10y = 1.10
- Subtract the second equation from the modified first equation:
(0.20x + 0.10y) - (0.20x + 0.05y) = 1.10 - 0.55
0.05y = 0.55
y = 11
- Substitute the value of y into one of the original equations to find x:
0.10x + 0.05(11) = 0.55
0.10x + 0.55 = 0.55
0.10x = 0
x = 0
Based on these calculations, the number of dimes (x) would be 0 and the number of nickels (y) would be 11.
Please keep in mind that these solutions are based on the given equations and information provided. If there are any errors or missing details, the solutions may change.