Let x be the cost of 1 pen
then cost of 1 notebook = x + 8.20
Let y be the number of pens Tan buys
then number of notebooks Tan buys = y/4
She spent $26 more on books than on pens which means
Cost of notebooks - Cost of pens = 26
(x + 8.20) * y/4 - xy = 26
Sinplifying it
(xy + 8.20y)/4 - xy = 26
(xy + 8.20y - 4xy)/4 = 26
8.20y - 3xy = 104
She spent $394 which means
Cost of notebooks + Cost of pens = 394
(x + 8.20) * y/4 + xy = 394
Simplifying it
(xy + 8.20y)/4 + xy = 394
(xy + 8.20y + 4xy)/4 = 394
8.20y + 5xy = 1576
Now, we have two equations,
(1) 8.20y - 3xy = 104
(2) 8.20y + 5xy = 1576
Now we need to find a third equation with either x or y as the subject of any of both the previous equations.
Let's make y the subject of (2) equation
8.20y + 5xy = 1576
y(8.20 + 5X) = 1576
(3) y = 1576/(8.20 + 5x)
Let's substitute the new value of y from (3) into (1) because we rearranged (2) to from (3)
8.20y - 3xy = 104
y(8.20 - 3x) = 104
y = 104/(8.20 - 3x)
1576/(8.20 + 5x) = 104/(8.20 - 3x)
1576 * (8.20 - 3x) = 104 * (8.20 + 5x)
12923.2 - 4728x = 852.8 + 520x
12923.2 - 852.8 = 4728x + 520x
12070.4 = 5248x
12070.4/5248 = x
x = 2.3
Now find the value of y by substituting the value of x in either equation, preferably (3)
y = 1576/(8.20 + 5x)
y = 1576/(8.20 + 5 * (2.3))
y = 80
Therefore cost of 1 notebook = x + 8.20 = 2.3 + 8.20 = $10.50
A rhombus has four equal sides. If the perimeter of this rhombus is 164, then the length of one side is 164/4, or 41.
Draw this rhombus. Label all four sides with "41." Label the longer diagonal 80 and the half length of that diagonal 40. You will see inside the rhombus four congruent triangles with hypotenuse 41, leg 10 and unknown height. Thus, this unknown height is found by solving x^2 + 40^2 = 41^2, and x^2=9, so that the length of the shorter diagonal is 2(2) = 18 (answer).
Answer:
Habrá 100 chocolates en total en 5 cajas de chocolates.
Step-by-step explanation:
Esta pregunta es resolvida usando proporciones, con lo uso de regla de tres
.
11 cajas, 220 chocolates:
Entonces:
20 chocolates por caja.
Calcula cuántos chocolates habrá en total en 5 cajas de chocolates.
20 chocolates por caja, entonces:
5*20 = 100
Habrá 100 chocolates en total en 5 cajas de chocolates.
