Its the connection between those numbers
The formula for that area would be A=1/2xbxh so you would do A=1/2x3.5x3 and that equals 5.25
(1) x+y+z=1300
(2) x+y=780 => x = 780 - y
(3) y+z=850 => z = 850 - y
Replace x and z with y in function (1)
780 - y + y + 850 - y = 1300
1630 - y = 1300
y = 330
Therefore, x = 780 - y = 780 - 330 = 450
z = 850 - y = 850 - 330 = 520
Dave can do 450 catalog orders per day
Frank can do 330 catalog orders per day
Kathy can do 520 catalog orders per day
Answer: A scone costs $2.64, and a large coffee costs $1.92.
Explanation: We can write both scenarios as equations, and write it as a system of equations.
“Luis picked up seven scones and four large coffees. He paid $26.16.”
Let’s express the cost of a scone as x.
Let’s express the cost of a large coffee as y.
The first equation would be 7x + 4y = 26.16.
“Rachel picked up six scones and five large coffees. She paid $25.44.”
Let’s express the cost of a scone as x.
Let’s express the cost of a large coffee as y.
The second equation would be 6x + 5y = 25.44.
The systems of equations is:
7x + 4y = 26.16
6x + 5y = 25.44
Let’s take the first equation and solve for x.
7x + 4y = 26.16
7x = 26.16 - 4y
x = (26.16 - 4y)/7
Let’s substitute x in the second equation for (26.16 - 4y)/7, and solve for y.
6((26.16 - 4y)/7) + 5y = 25.44
Distribute the 6 across 26.16 - 4y in the term 6((26.16 - 4y)/7).
(156.96 - 24y)/7 + 5y = 25.44
Rewrite 5y as 35y/7 so it has a common denominator with (156.96 - 24y)/7.
(156.96 - 24y)/7 + 35y/7 = 25.44
Combine like terms.
(156.96 + 11y)/7 = 25.44
Multiply both sides by 7.
156.96 + 11y = 178.08
Subtract 156.96 from both sides.
11y = 21.12
Divide both sides by 11.
y = 1.92
Substitute y into the first equation.
7x + 4(1.92) = 26.16
Simplify 4(1.92).
7x + 7.68 = 26.16
Subtract 7.68 from both sides.
7x = 18.48
Divide both sides by 7.
x = 2.64
Since x = 2.64, we know that the cost of a scone is $2.64.
Since y = 1.92, we know that the cost of a large coffee is $1.92.
Therefore, a scone costs $2.64, and a large coffee costs $1.92.
