There are two ways of scoring points in a ball game: a ‘major’ scores 5 points and a ‘minor’
scores 3 points.
In a match played yesterday, the Reds beat the Blues 77–52 despite the fact that the Blues
scored exactly twice as many majors as minors, whilst the Reds scored exactly half as many
majors as minors.
How many majors were scored altogether in yesterday’s match?
Hi, how do I do this? Thank you so much in advance!
If the Reds scored x majors and y minors,
5x+3y = 77
y = 2x
So, x=7, y=14
If the Blues scored x majors and y minors, then
5x+3y = 52
x = 2y
y=4, x=8
7+8 = 15
also, 14+4=18, and 5*15 + 3*18 = 77+52
To solve this problem, let's assign variables to unknown quantities:
Let's say the number of majors scored by the Blues is B_majors, and the number of minors scored by the Blues is B_minors.
Similarly, let's say the number of majors scored by the Reds is R_majors, and the number of minors scored by the Reds is R_minors.
We are given the following information:
1. The Reds beat the Blues with a score of 77-52.
2. The Blues scored exactly twice as many majors as minors.
3. The Reds scored exactly half as many majors as minors.
Based on these clues, we can write the following equations:
1. B_majors * 5 + B_minors * 3 = 52 --> (equation 1)
2. R_majors * 5 + R_minors * 3 = 77 --> (equation 2)
3. B_majors = 2 * B_minors --> (equation 3)
4. R_majors = 1/2 * R_minors --> (equation 4)
We can use these equations to solve for the unknowns.
First, let's solve equations 3 and 4 to express the variables B_majors and R_majors in terms of B_minors and R_minors:
From equation 3, B_majors = 2 * B_minors
From equation 4, R_majors = 1/2 * R_minors
Substituting these expressions into equation 2, we have:
2 * B_minors * 5 + B_minors * 3 = 52
10 * B_minors + 3 * B_minors = 52
13 * B_minors = 52
B_minors = 4
Now, substitute the value of B_minors into equation 3 to solve for B_majors:
B_majors = 2 * B_minors
B_majors = 2 * 4
B_majors = 8
Substitute the value of B_majors into equation 1 to solve for R_minors:
R_minors = 2 * B_majors
R_minors = 2 * 8
R_minors = 16
Finally, substitute the value of R_minors into equation 4 to solve for R_majors:
R_majors = 1/2 * R_minors
R_majors = 1/2 * 16
R_majors = 8
Therefore, the total number of majors scored in yesterday’s match is B_majors + R_majors = 8 + 8 = 16.
To solve this problem, we can start by setting up equations based on the given information and then solve them to find the answer.
Let's assume the number of majors scored is 'M' and the number of minors scored is 'm'.
According to the given information, the Reds scored exactly half as many majors as minors. So we can write the equation as:
Reds' majors = (1/2) * Red minors
M = (1/2) * m
The Blues scored exactly twice as many majors as minors. So we can write the equation as:
Blues' majors = 2 * Blue minors
M = 2 * m
Now, we know that each major scores 5 points and each minor scores 3 points. So we can write the equation for the total points scored by each team as:
Reds' total points = 5 * M + 3 * m
Blues' total points = 5 * 2 * m + 3 * m
We are given that the Reds beat the Blues 77-52, so the equation for the total points can be written as:
5 * M + 3 * m = 77
5 * 2 * m + 3 * m = 52
Now we have a system of two equations with two variables. We can solve these equations to find the values of 'M' and 'm'.
First, we can simplify the second equation:
10m + 3m = 52
13m = 52
m = 4
Now substitute this value of 'm' in the first equation:
M = (1/2) * m
M = (1/2) * 4
M = 2
So, the number of majors scored altogether in yesterday’s match is 2.
Therefore, in yesterday's match, the Reds scored a total of 2 majors.
Well, let's do some clown math to figure this out! So we know that the Blues scored exactly twice as many majors as minors, and the Reds scored exactly half as many majors as minors.
Let's call the number of minors scored by the Blues "Bm" and the number of majors scored by the Blues "Bj". Similarly, let's call the number of minors scored by the Reds "Rm" and the number of majors scored by the Reds "Rj".
According to the information given, we know that:
Bj = 2Bm (The Blues scored twice as many majors as minors)
Rj = (1/2)Rm (The Reds scored half as many majors as minors)
Now, let's think about the points scored. A major scores 5 points and a minor scores 3 points.
For the Blues, the total score is calculated as:
Bj * 5 + Bm * 3 = 77
For the Reds, the total score is calculated as:
Rj * 5 + Rm * 3 = 52
Now we can use this information to solve the equations and find the number of majors scored altogether. But given that this is a clown bot, I think I'll let you have some fun figuring out the solution yourself! Enjoy the math puzzle!
r = Reds' majors , b = Blues' majors
Blues ... 5 b + (3 b / 2) = 52
... 10 b + 3 b = 104
... b = ?
Reds ... 5 r + (3 * 2 * r) = 77
... 5 r + 6 r = 77
... r = ?
r + b = ?