Any time you have a fraction within an equation, multiply the entire equation by the denominator to clear the fraction. Since the lead term is negative, we can multiply that away as well
(-14) (0=-1/14x²+4x+5) [now distribute]
0=x²-56x+70 [try to factor into binomials first]
Since 70 only has prime factors of 2·5·7, there is no combination which equals (-56). Use the quadratic formula, or complete the square. I'll use quadratic:
x=<u>-b+/-√(b²-4ac)</u>
2a
a=1, b=(-56), c=70
x= <u>-(-56)+/- √((-56)²-4(1)(70)</u>
2(1)
x= <u>56+/- √(3136-280)
</u> 2
<u />x=<u>56+/-√(2856)</u>
2
x=<u>56+/-√(2³·3·119)</u>
2
x=<u>56+/-2√(714)</u>
2
x=28+√714; x=28-√714
Combining the numbers, we get 3w+12=5
3w=-7
w=-7/3
Answer:
The number of Carmel muffins is 8 and the number of lemon muffins is 12.
Step-by-step explanation:
Melvin Marshall bought a total of 20 Muffins . Some were camel-glazed muffins and some were lemon. The Carmel muffins cost $3 each while the lemons cost $2.5 . The number of carmel muffins and lemon muffins can be calculated as follows
total number of muffin = 20
Let
a = number of carmel - glazed muffins
b = number of lemon muffins
a + b = 20.............(i)
The total cost
3a + 2.50b = 54................(ii)
Combine the equations
a + b = 20.............(i)
3a + 2.50b = 54................(ii)
a = 20 - b
insert the value of a in equation (ii)
3(20 - b) + 2.50b = 54
60 - 3b + 2.50b = 54
60 - 54 = 0.5b
0.5b = 6
divide both sides by 0.5
b = 6/0.5
b = 12
Insert the value of b in equation (i)
a + b = 20.............(i)
a + 12 = 20
a = 20 - 12
a = 8
The number of Carmel muffins is 8 and the number of lemon muffins is 12.
