Ahmed sells different types of cake in his shop. The cost of each cake depends on its type and its size. Every small cake costs $$\(\$ x\)$$ and every large cake costs $$\(\$(2 x+1)\)$$. Petra spends $$\(\$ 20\)$$ on small coffee cakes and $$\(\$ 10\)$$ on large coffee cakes. The total number of cakes is 45 . Write an equation in terms of $$\(x\)$$. Solve this equation to find the cost of a small coffee cake. Show all your working. $$\(\$\)$$ ............................................
Exam No：0580_w20_qp_42 Year：2020 Question No：5(d)
Answer:
\(\frac{20}{x}+\frac{10}{2 x+1}=45\) oe
\(90 x^{2}-5 x-20[=0]\) oe
\((9 x+4)(2 x-1)[=0]\) or for
\(\frac{--1 \pm \sqrt{(-1)^{2}-4(18)(-4)}}{2(18)}\) oe
\([0] .5\) or \(\frac{1}{2}\) final answer
\(90 x^{2}-5 x-20[=0]\) oe
\((9 x+4)(2 x-1)[=0]\) or for
\(\frac{--1 \pm \sqrt{(-1)^{2}-4(18)(-4)}}{2(18)}\) oe
\([0] .5\) or \(\frac{1}{2}\) final answer
Knowledge points:
E2.3.1 Manipulate algebraic fractions.
E2.3.2 Factorise and simplify rational expressions.
E2.5.4 Derive and solve quadratic equations by factorisation, completing the square and by use of the formula.
Solution:
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