Please help me with steps to work out the following problem. Simplist way possible.
Mary needed different coloured balloons for decoration. She had $1.25 (Australian dollars) and spent it all on a number of white, red, and blue balloons. A white balloon costs $.10, a red one $.15 and a blue one $.05. She bought one white balloon less than the red and the total number of white and red balloons equals the number of blue ones. How many of each colour doc Mary buy?
Thank you :)
let number of reds be x
number of whites = x-1
number of blues = x + x-1 = 2x - 1
now to the value of these:
.15x + .10(x-1) + .05(2x-1) = 125
times 100
15x + 10(x-1) + 5(2x-1) = 12500
solve for x, and sub back in my definitions
To solve this problem, let's break it down into steps:
Step 1: Assign variables
Let's assign variables to represent the unknown quantities in the problem. Let's say,
W = number of white balloons
R = number of red balloons
B = number of blue balloons
Step 2: Set up equations
From the problem statement, we can gather the following information:
- The cost of a white balloon is $0.10, so the total cost of white balloons is 0.10W.
- The cost of a red balloon is $0.15, so the total cost of red balloons is 0.15R.
- The cost of a blue balloon is $0.05, so the total cost of blue balloons is 0.05B.
- Mary spent $1.25 in total, so the equation for the total cost is:
0.10W + 0.15R + 0.05B = 1.25
- Mary bought one less white balloon than red balloons, so the equation for the white and red balloons is:
W = R - 1
- The total number of white and red balloons equals the number of blue balloons, so the equation for the balloons is:
W + R = B
Step 3: Simplify the equations
We can simplify the equations further by replacing W with (R-1) in the second equation to get:
(R-1) + R = B
2R - 1 = B
Step 4: Solve the equations
Now we have two equations:
0.10W + 0.15R + 0.05B = 1.25
2R - 1 = B
We can use substitution method or elimination method to solve these equations. Since the second equation is already solved for B, let's substitute it in the first equation:
0.10W + 0.15R + 0.05(2R - 1) = 1.25
0.10W + 0.15R + 0.10R - 0.05 = 1.25
0.10W + 0.25R - 0.05 = 1.25
0.10W + 0.25R = 1.30
Now, substitute the value of W from the second equation (W = R - 1) in the above equation:
0.10(R - 1) + 0.25R = 1.30
0.10R - 0.10 + 0.25R = 1.30
0.35R - 0.10 = 1.30
0.35R = 1.40
R = 1.40 / 0.35
R = 4
Substitute the value of R in the second equation (W = R - 1):
W = 4 - 1
W = 3
Finally, substitute the values of W and R in the third equation (W + R = B):
3 + 4 = B
B = 7
So, Mary bought 3 white balloons, 4 red balloons, and 7 blue balloons.