Question

Flour costs $0.80 per pound and sugar costs $0.50 per pound. An order of flour and sugar weighs 15 pounds and costs $9.00. Make a system of equations?

Please help I really need your help.

Answer 1

Of course! Let's tackle this problem step by step to create a system of equations that will help us find out how much flour and sugar are in the order.

Let's start by defining the variables:
- Let x represent the pounds of flour in the order.
- Let y represent the pounds of sugar in the order.

Now we'll use the information given to create the equations for our system:

1. The total weight of the order is 15 pounds:
This means that when you add the pounds of flour (x) to the pounds of sugar (y), the sum must be 15 pounds. So, our first equation is:
x + y = 15

2. The total cost of the order is $9.00:
Flour costs $0.80 per pound, and sugar costs $0.50 per pound. So, the cost of the flour will be 0.80 (dollars per pound) times x (pounds), and the cost of the sugar will be 0.50 (dollars per pound) times y (pounds). The sum of these costs must equal $9.00. So, our second equation is:
0.80x + 0.50y = 9.00

Now, we have our system of two equations with two unknowns:
1) x + y = 15
2) 0.80x + 0.50y = 9.00

Let's solve this system of equations. One method we can use is substitution or elimination. Given the nature of the equations, it looks easier to use the elimination method.

We can multiply the entire first equation by 0.50 (which is the cost per pound of sugar) to help us eliminate y:

0.50(x + y) = 0.50(15)
0.50x + 0.50y = 7.50

Now we have a modified system of equations:
1) 0.50x + 0.50y = 7.50
2) 0.80x + 0.50y = 9.00

Subtract the first modified equation (1) from the second equation (2) to eliminate y:
(0.80x + 0.50y) - (0.50x + 0.50y) = 9.00 - 7.50
0.80x - 0.50x + 0.50y - 0.50y = 1.50
0.30x = 1.50

Divide both sides of this last equation by 0.30 to solve for x:
x = 1.50 / 0.30
x = 5

Now that we know x, we can substitute x back into one of our original equations to find y. Let's substitute x = 5 into the first equation:

x + y = 15
5 + y = 15
y = 15 - 5
y = 10

So, the order consists of 5 pounds of flour and 10 pounds of sugar.

Answer 2

Answer:
`x+y=15`

`0.80x+0.50y=9`

Explanation:

Let x be the amount of flour and y be the amount of sugar ordered.

Since, the order of flour and sugar weighs 15 pounds.

Therefore,
`x+y=15`

Also, Flour costs $0.80 per pound and sugar costs $0.50 per pound.

The cost of ordered flour=$0.80x

The cost of ordered sugar=$0.50y

Now, the total cost of the order=
`0.80x+0.50y=9`

Hence, for the given situation the system of equations is:-

`x+y=15`

`0.80x+0.50y=9`