Answer:
Lines are
Cost = 10x + 10
Cost = 4x + 40
Solution is (5, 60) when both costs are the same
Explanation:
Let x be the number of charms on the bracelet
We will represent the cost of the bracelet with charms for purchasing from Yardley as $Y
Since it costs a fixed amount of $10 for the bracelet and $10 per charm
Y = 10x + 10
Let us represent the cost of the bracelet with charms for purchasing from Hardin as $H
Since it costs a fixed amount of $40 for the bracelet and $4per charm
H= 4x + 40
Therefore the two equations for this situation are
Y = 10x + 10 [1]
H = 4x + 40 [2]
To graph this , take two values for x in each equation, find the corresponding cost . That will give you two points;. Draw a line through these two points for each equation
For Y = 10x + 10
Choose x = 0 to get Y = 10. Y= 10(0) + 10 = 10
Thus point(0, 10) is one point
Choose another value for x, say x = 3: Y = 10(3) + 10 = 30 + 10 = 40
The other point is (3, 40)
Draw a straight line through these two points
For H = 4x + 40:
x = 0 ==> 4(0) + 40 ==> (0, 40) as one point
x = 10 ==> 4(10) + 40= 80 ==> (4, 80) is another point
Draw a straight line thru these two points
The point of intersection of these two lines from the graph is (5, 60)
This represents the number of charms from both places where the cost is the same
We can solve this mathematically as follows
Set [1] = [2]
10x + 10 = 4x + 40
10x - 4x = 40 - 10
6x = 30
x = 5
Substituting x = 5 in any of the equations will give the cost
Y(5) = 10(5) + 10 = 60
H(5) = 4(5) + 40 = 60