Slot method
5 slots
1st slot: 20
2nd slot: 19 (1 went to first slot)
3rd slot: 18
4th slot: 17
5th slot: 16
20*19*18*17*16=186,040 ways
It is 1.55 times the value of the second number.
The first thing you want to do is plug in x and y into both equations:
a(3) + b(4) = 4
b(3) + a(4) = 8
rearrange to line up a’s and b’s
3a + 4b = 4
4a + 3b = 8
now you want to choose a or b and multiply each equation by a number to make them have the same amount of a’s or b’s.
4(3a + 4b = 4) = 12a + 16b = 16
3(4a + 3b = 8) = 12a + 9b = 24
Now we subtract the bottom equation from the top and solve for b:
12a + 16b - (12a + 9b) = 16 - 24
7b = -8
b = -8/7
Now we plug back in for b to one of the original equations:
3a + 4(-8/7) = 4
3a + (-32/7) = 4
3a - (32/7) = 4
3a = 4 + (32/7)
3a = (28/7) + (32/7)
3a = 60/7
a = (60/7)/3 = 20/7.
Finally, plug a and b in together to double check using the second equation.
4a + 3b = 8
4(20/7) + 3(-8/7) = ?
(80/7) - (24/7) = ?
56/7 = 8.
Let the amount Kevin earns be represented with K
Let the amount Jason earns be represented with J
Jason earns $32.50 less than twice Keyin earns can be represented by
J = K - 32.5 ----- equation 1
Jason earns $ 212.5
J = 212.5 ----- equation 2
From equation 1, we can write the equation to solve for what Kevin earns
J = K - 32.5
Making K the subject of the formula
K = J + 32.5
Putting J = 212.5 into the equation above
K= $ 212.5 + $ 32.5
K = $ 245
Kevin earns $245
I'll write the equation again with the blanks filled in.
1/2 of 2/3 = 1/2 of two thirds = one third
2/3 is read as two thirds.
Half of 2/3 is 1/3, because 1/3+1/3=2/3
Hope this helps!
