A package of 12 hex bolts and 10 anchor bolts weighs 7 pounds. A second package of 5 hex bolts and 15 anchor bolts weighs 4 pounds. A single hex bolt weighs ___________pounds, rounded to one decimal place.
0.2
To find the weight of a single hex bolt, we need to set up a system of equations using the information given.
Let's assume the weight of a single hex bolt is "x" pounds.
From the first package, we have 12 hex bolts, so their total weight would be 12x pounds.
Similarly, we have 10 anchor bolts in the first package, with each weighing "y" pounds. So the total weight of the anchor bolts would be 10y pounds.
From the second package, we have 5 hex bolts, so their total weight would be 5x pounds.
And we have 15 anchor bolts in the second package, with each weighing "y" pounds. So the total weight of the anchor bolts would be 15y pounds.
According to the information given, the total weight of the first package (hex bolts + anchor bolts) is 7 pounds. So we have the equation:
12x + 10y = 7
Similarly, the total weight of the second package (hex bolts + anchor bolts) is 4 pounds. So we have the equation:
5x + 15y = 4
We now have a system of two equations with two variables. To solve this system, we can use any method such as substitution or elimination to determine the value of "x" (the weight of a single hex bolt).
Let's use the method of substitution. From the first equation, we can isolate "y" in terms of "x":
10y = 7 - 12x
y = (7 - 12x)/10
Now substitute this value of "y" into the second equation:
5x + 15((7 - 12x)/10) = 4
Simplifying this equation will give us a value for "x", which is the weight of a single hex bolt.
12h+10a = 7
5h+15a = 4
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