Let
x = pounds of peanuts
y = pounds of cashews
z = pounds of Brazil nuts.
The total pounds is 50, therefore
x + y + z = 50 (1)
The total cost is $6.60 per pound for 50 pounds of mixture.
The total is equal to the sum of the costs of the different nuts.
Because the cost for peanuts, cashews, and Brazil nuts are $3, $10, and $9 respectively, therefore
3x + 10y + 9z = 50*6.8
3x + 10y + 9z = 340 (2)
There are 10 fewer pounds of cashews than peanuts, therefore
x = y + 10 (3)
Substitute (3) into (1) and (2).
y + 10 + y + z = 50
2y + z = 40 (4)
3(y + 10) + 10y + 9z = 340
13y + 9z = 310 (5)
From (4),
z = 40 - 2y (6)
Substitute (6) into (5).
13y + 9(40 - 2y) = 310
-5y = -50
y = 10
z = 40 - 2y = 40 - 20 = 20
x = y + 10 = 20
Answer:
Peanuts: 20 pounds
Cashews: 10 pounds
Brazil nuts: 20 pounds
Answer:
24
Step-by-step explanation:
(10-1) x 2 + 2 x 3
9 x 2 + 6
18 + 6
24
Answer:
y = 8
x = 8√5
z = 4√5
Step-by-step explanation:
Using the formula (which is a geometric mean):
a y
---- = -----
x a
Where a is the altitude (y), x is a projection (16), and y is the other projection (4):
y 4
---- = -----
16 y
Cross multiply:
y² = 16 (4)
y² = 64
√y² = √64
y = 8
To find x and z, use the Pythagorean Theorem:
16² + y² = x²
256 + 8² = x²
256 + 64 = x²
320 = x²
√320 = √x²
√64√5 = √x²
8√5 = x
x = 8√5
4² + y² = z²
16 + 64 = z²
80 = z²
√80 = √z²
√16√5 = √z²
4√5 = z
z = 4√5
Answer:
3/8
Step-by-step explanation:
With unlike denominators find the Least Common Denominator (LCD)
LCD = 8
Multiplying numerators and denominators to get the LCD in all fraction denominators
=3/4 times 2/2−3/8
Then rewriting the equation with the equivalent fractions
=6/8−3/8
With like denominators we can operate on just the numerators
=6−3/8
=3/8
