Answer: <u>4 pounds</u> of brand X sugar
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Reason:
n = number of pounds of brand X sugar
5n = cost of buying those n pounds, at $5 per pound
Brand Y costs $2 per pound, and you buy 8 lbs of it, so that's another 2*8 = 16 dollars.
5n+16 = total cost of brand X and brand Y combined
n+8 = total amount of sugar bought, in pounds
3(n+8) = total cost because we buy n+8 pounds at $3 per pound
The 5n+16 and 3(n+8) represent the same total cost.
Set them equal to each other. Solve for n.
5n+16 = 3(n+8)
5n+16 = 3n+24
5n-3n = 24-16
2n = 8
n = 8/2
n = 4 pounds of brand X sugar are needed
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Check:
n = 4
5n = 5*4 = 20 dollars spent on brand X alone
16 dollars spent on brand Y mentioned earlier
20+16 = 36 dollars spent total
n+8 = 4+8 = 12 pounds of both types of sugar brands combined
3*12 = 36 dollars spent on both types of sugar brands
The answer is confirmed.
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Another way to verify:
5n+16 = 3(n+8)
5*4+16 = 3(4+8)
20+16 = 3(12)
36 = 36
Answer:
12;16
Step-by-step explanation:
The Pythagorean theorem states that
a^2+b^2=c^2 where a and b are legs of a triangle, and c is the hypotenuse.
This means that we have to find 2 values that once squared, add up to 400. (20^2)
Based on this, we can use the values of 12 and 16 to satisfy this.
12^2+16^2=144*256=400
Therefore, the legs of the triangle are 12 and 16.
M 1: 64
M 2: 49
M 3: 87
M 4: 44
Answer:
Speed of the biker is 13 mph and that of wind is 1 mph.
Step-by-step explanation:
Given:
Time taken by the biker to cover a distance is 7 hrs when he was travelling against the speed of the wind.
Time taken to cover same distance is 6 hours when he was travelling with the speed of the wind.
We have to find the speed of the biker and that of the wind.
Let the speed of the biker is "b" mph
And the speed of the wind is "w" mph
As we know:
Distance = Product of speed and time
Re-arranging the above situation in terms of equation.
⇒ 
⇒ 
⇒ 
...(i) ⇒ 
...(ii)
Multiplying equation (i) with 6 and equation (ii) with 7 so that we can eliminate one variable that is "w" after adding both the equation.
⇒ 
equation (iii)
⇒ 
equation (iv)
⇒ Adding both the equations.
⇒ 
⇒ 
⇒ 
mph.
Speed of the biker is 13 mph.
⇒ Plugging b=13 in equation (ii),we have:
⇒
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
mph.
Speed of the biker is 13 mph and the speed of the wind is 1 mph whenever the biker is with the speed of the wind the biker's speed increases by 1 mph and subsequently decreases when he is against the speed of the wind.
Answer:
x = 7
Step-by-step explanation:
Solve for x over the real numbers:
(3 x)/(2 x - 2) = 14/8
14/8 = 7/4:
(3 x)/(2 x - 2) = 7/4
Cross multiply:
12 x = 7 (2 x - 2)
Expand out terms of the right hand side:
12 x = 14 x - 14
Subtract 14 x from both sides:
-2 x = -14
Divide both sides by -2:
Answer: x = 7
