in their championship game the eastside golden eagles scored

in their championship game, the eastside golden eagles scored 60 points on a combination of two-point shots and three-point shots. if they made a total of 27 shots, how many of each kind of shot was made?

Solution

Let us assume that the eastside golden eagles made x number of 2 point shots and y number of 3 point shots. Then, we have

x + y = 27...(1) and 2x + 3y = 60. ... (2) On multiplying both the sides of the 1st equation by 2 and then subtracting the result from the 3rd equation, we have 2x + 3y - 2(x + y) = 60 - 2*27 or, 2x + 3y - 2x - 2y = = 60 - 54, or

y = 6 . Since x + y = 27, we have x = 27 - 6 = 21. We can verify this result by substituting x = 21 and y = 6 in the 2nd equation. On substitution, we have 2x + 3y = 2*21 + 3*6 = 42 + 18 = 60 which is correct. Therefore, the eastside golden eagles made 21 two point shots and 6 three point shots.