Answer: [tex]17\ lb[/tex]
Step-by-step explanation:
Let be "l" the weight in pounds of the lighter bag and "h" the weigth in pounds of the havier bag.
These bags have a total weight of 27 pounds. Then:
[tex]l+h=27[/tex] [Equations 1]
If 1 pound is added to the heavier bag and 1 pound is removed from the lighter bag, the heavier bag will weigh twice as much as the lighter bag. This is:
[tex]h+1=2(l-1)[/tex] [Equation 2]
Then, in order to find the weight of the heavier bag, the steps are:
-Solve for "l" from [Equations 1]:
[tex]l+h=27\\\\l=27-h[/tex]
- Substitute the equation obtained into the [Equations 2] and solve for "h":
[tex]h+1=2((27-h)-1)\\\\h+1=2(26-h)\\\\h=52-2h-1\\\\3h=51\\\\h=\frac{51}{3}\\\\h=17[/tex]
ANSWER:
The weight of heavier bag is 17.33
SOLUTION:
Let the weight of heavier bag and lighter bag be a , b
Given that, two bags of flour have a total weight of 27lb
Hence we get a + b = 27 --- eqn (1)
And if 1lb is removed from the lighter bag, the heavier bag will weigh twice as much as the lighter bag.
Which means, a = 2(b-1) ---- eqn 2
Now, substitute a value in (1)
2(b-1) + b = 27
On multiplying the terms within the bracket we get
2b -2 + b = 27
3b = 27 + 2
3b = 29
b = [tex]\frac{29}{3}[/tex]
substitute the value of “b” in eqn 2
[tex]a=2\left(\frac{29}{3}-1\right)[/tex]
[tex]a=2\left(\frac{29-3}{3}\right)[/tex]
[tex]=2 \times \frac{26}{3}[/tex]
[tex]=\frac{52}{3}=17.33[/tex]
Hence, the weight of heavier bag is 17.33
