you have a space in your garden for 100 small flowering bulbs.
Crocus bulbs cost $0.45 each, and daffodil bulbs cost $0.85 each. Your budget allows you to spend $55.80 on bulbs. How many crocus bulbs and how many daffodil bulbs can you buy?
X Crocus bulbs.
Y Daffodil bulbs.
Eq1: X + Y = 100
Eq2: 0.45x + 0.85y = $55.80
Multiply Eq1 by (-0.85) and add the Eqs:
-0.85x - 0.85y = -85
+0.45x + 0.85y = 55.80
Sum: -0.40x = -29.2
X = 73
In Eq1, replace X with 73:
73 + Y = 100
Y = 27
Let's assume that you will buy x crocus bulbs and y daffodil bulbs.
The cost equation for the crocus bulbs is: 0.45x
The cost equation for the daffodil bulbs is: 0.85y
According to the given information, you have a budget of $55.80. So we can set up the equation:
0.45x + 0.85y = 55.80
Now, we know that you have space for 100 bulbs in total. So:
x + y = 100
To solve this system of equations, we will multiply the second equation by 0.45 to make the x coefficient the same:
0.45x + 0.45y = 45
Now we can subtract this equation from the first equation:
(0.45x + 0.85y) - (0.45x + 0.45y) = 55.80 - 45
0.40y = 10.80
To find the value of y, we divide both sides of the equation by 0.40:
y = 10.80 / 0.40
y = 27
Now we can substitute the value of y back into the second equation to find x:
x + 27 = 100
x = 100 - 27
x = 73
So, you can buy 73 crocus bulbs and 27 daffodil bulbs.
To solve this problem, we can set up a system of equations.
Let's assume that you buy x crocus bulbs and y daffodil bulbs.
The first equation represents the total number of bulbs: x + y = 100.
The second equation represents the total cost: 0.45x + 0.85y = 55.80.
To solve this system of equations, we can use the substitution method:
1. Rearrange the first equation to solve for x: x = 100 - y.
2. Substitute x in the second equation with 100 - y: 0.45(100 - y) + 0.85y = 55.80.
3. Simplify and solve for y:
45 - 0.45y + 0.85y = 55.80,
0.40y = 10.80,
y = 10.80 / 0.40,
y = 27.
4. Substitute y back into the first equation to find x: x + 27 = 100,
x = 100 - 27,
x = 73.
Therefore, you can buy 73 crocus bulbs and 27 daffodil bulbs.