Smile 發問於 科學及數學數學 · 2 月前

Maths problem: how to do, thanks?

2 個解答

• 2 月前
最愛解答

The current weight of beans is 32 g.

The current weight of rice is 50 - 32 = 18 g.

Suppose Fanny's claim is correct.

Then she adds 5k (in g) and 2k (in g) of rice and beans, respectively, to the mixture, where k is a positive constant.

The new weight of beans is (32 + 2k) g.

The new weight of rice is (18 + 5k) g.

Consider (18 + 5k):(32 + 2k) = 7:9.

9(18 + 5k) = 7(32 + 2k)

162 + 45k = 224 + 14k

31k = 62

k = 2

Because the value of k can be solved as a positive constant, Fanny's claim is correct and agreed.

Note:

If k cannot be solved, or k is solved to be a non-positive number, then the claim is not agreed.

• SC147
Lv 6
2 月前

Suppose Fanny adds 5x g rice & 2x g beans so that wt. of rice:beans=7:9

(18+5x):(32+2x) = 7:9

18+5x 　 7

--------- = ---

32+2x  　9

7(32+2x) = 9(18+5x)

224+14x = 162+45x

224-162 = 45x-14x

62 = 31x

∴ x = 2

Yes, I agree that she can add 5(2)=10 g rice & 2(2)=4 g beans

so that wt. of rice:wt. of beans = 7:9