Problem Solving

A college basketball team has won 60% of its games, with 15 games remaining on the season's schedule. If the team is to win at least 60% of its scheduled games for the entire season, at most how many of the remaining games can the team lose?
A. 6
B. 7
C. 8
D. 9
E. 10

A school supply store sells only one kind of desk and one kind of chair, at a uniform cost per desk or per chair. If the total cost of 3 desks and 1 chair is twice that of 1 desk and 3 chairs, then the total cost of 4 desks and 1 chair is how many times that of 1 desk and 4 chairs?
A. 5
B. 3
C. 8/3
D. 5/2
E. 7/3

Answer is A.

One way to do it: assume the basketball team is 6-4 (having played 10 games thus far). For them to finish the season with at least a 60% winning pct, they must win 9 and lose 6.

Set up a proportion. Let x=number of games won. x/25 (25 is total games played) must equal 6/10 and solve for x. x=15, so they must win 15, meaning from now they must win 9 to finish at 15-10 (60% winning pct).

Answer is E.

Two equations:
3D+C=2(D+3C) ----1
4D+C=X(D+4C) ----2

From 1, we know D=5C. Plug that into 2 to get x=7/3.

If that's correct, hope it helps!

jamesk486 wrote:A college basketball team has won 60% of its games, with 15 games remaining on the season's schedule. If the team is to win at least 60% of its scheduled games for the entire season, at most how many of the remaining games can the team lose?
A. 6
B. 7
C. 8
D. 9
E. 10

And for the equation inclined...

(0.6x + y) / (x + 15) = 0.6

Solving for y we get 9.

So, 6 games can be lost to still hit the 60% mark

(0.6x + y) / (x + 15) = 0.6 ==> can u explain the equation for me pls? thanks!

jamesk486 wrote:(0.6x + y) / (x + 15) = 0.6 ==> can u explain the equation for me pls? thanks!

The equation is setup to yield percent of games won (hence the 0.6, or 60%, on the right side of the equal sign). So let's start off looking at the information we have:

1) We know that the team has won 60% of its games thus far, but we don't know how many games they've played. We'll say the number of games played = 'x'.

2) We know they need to win a certain amount of the rest of their games in order to hit the 60% winning percentage for the season. We'll say the number of games needed to win in order hit that percentage = 'y'.

3) Now, we have .6x + y in the numerator which tells us total games won. What goes in the denominator? Well, if we want a percentage, we need to divide the total games won by TOTAL games. But we have no idea how many games they played, right? Actually, that's been defined in the question and in step 1. The've played 'x' games so far and they have 15 games left. So the denominator is 'x+15'.

Now, we have the equation: (.6x+y)/(x+15)=.6

Multiply both sides by (x+15) and you get: .6x+y=.6(x+15)

Now we have a .6x on both sides - they cancel out and y=.6(15) = 9

9 is the number of games they have to win in order to reach 60%, so how many games can they lose? 15 games left - 9 wins = 6 losses

Hope that helps.

A college basketball team has won 60% of its games, with 15 games remaining on the season's schedule. If the team is to win at least 60% of its scheduled games for the entire season, at most how many of the remaining games can the team lose?
A. 6
B. 7
C. 8
D. 9
E. 10

60/100 * 15 = 3/5 * 15 = 9 games have to be won...So it can loose 15-9 = 6 games...Hence A

A school supply store sells only one kind of desk and one kind of chair, at a uniform cost per desk or per chair. If the total cost of 3 desks and 1 chair is twice that of 1 desk and 3 chairs, then the total cost of 4 desks and 1 chair is how many times that of 1 desk and 4 chairs?
A. 5
B. 3
C. 8/3
D. 5/2
E. 7/3

3x + y = 2 (x+3y)
3x + y = 2x + 6y
x = 5y
Hence cost of 1 desk = Cost of 5 chairs

4x+y = 4(5y) + y = 21y
x+4y = 5y+4y = 9y
21y/9y = 7/3
Hence E