Let x represent the number of pounds of $10.75/lb coffee used in the mix.
.. 10.75x +3.25(100 -x) = 5.65*100 . . . . . . total cost of coffee blend
.. x(10.75 -3.25) = 100*(5.65 -3.25) . . . . . .separate x-terms from non-x terms
.. x = 240/7.5 = 32
32 pounds of $10.75/lb coffee should be used
68 pounds of $3.25/lb coffee should be used
Answer:
The point-slope formula states:
(
y
−
y
1
)
=
m
(
x
−
x
1
)
Where
m
is the slope and
(
x
1
y
1
)
is a point the line passes through.
Substituting the slope and values from the point in the problem gives:
(
y
−
−
1
)
=
3
5
(
x
−
−
3
)
(
y
+
1
)
=
3
5
(
x
+
3
)
If you want the equation in the somewhat more familiar slope-intercept form we can solve this equation for
y
. The slope-intercept form of a linear equation is:
y
=
m
x
+
b
Where
m
is the slope and
b
is the y-intercept value.
y
+
1
=
(
3
5
⋅
x
)
+
(
3
5
⋅
3
)
y
+
1
=
3
5
x
+
9
5
y
+
1
−
1
=
3
5
x
+
9
5
−
1
y
+
0
=
3
5
x
+
9
5
−
5
5
y
=
3
5
x
+
4
5
The point-slope formula states:
(
y
−
y
1
)
=
m
(
x
−
x
1
)
Where
m
is the slope and
(
x
1
y
1
)
is a point the line passes through.
Substituting the slope and values from the point in the problem gives:
(
y
−
−
1
)
=
3
5
(
x
−
−
3
)
(
y
+
1
)
=
3
5
(
x
+
3
)
If you want the equation in the somewhat more familiar slope-intercept form we can solve this equation for
y
. The slope-intercept form of a linear equation is:
y
=
m
x
+
b
Where
m
is the slope and
b
is the y-intercept value.
y
+
1
=
(
3
5
⋅
x
)
+
(
3
5
⋅
3
)
y
+
1
=
3
5
x
+
9
5
y
+
1
−
1
=
3
5
x
+
9
5
−
1
y
+
0
=
3
5
x
+
9
5
−
5
5
y
=
3
5
x
+
4
5
Step-by-step explanation:
To solve any algebraic equation, we want to get x by itself. Here, x is accompanied by 3.6. So that means we have to get rid of 3.6. To get rid of 3.6, one can either subtract 3.6 from both sides or add -3.6 to each side.
