iGCSE Mathematics (0580) - C2.5 Equations- Exam Style Questions Paper 1- New Syllabus
▶️ Answer/Explanation
Let \(a\) = cost of one apple (\$) and \(p\) = cost of one pear (\$).
Set up the two equations:
\[15a + 10p = 42.5 \quad \cdots (1)\]
\[4a + 5p = 16 \quad \cdots (2)\]
Multiply equation (2) by 2 to match the \(10p\) coefficient:
\[8a + 10p = 32 \quad \cdots (3)\]
Subtract (3) from (1) to eliminate \(p\):
\[7a = 10.5 \implies a = 1.50\]
Substitute back into (2): \(4(1.5) + 5p = 16 \implies 6 + 5p = 16 \implies 5p = 10 \implies p = 2.00\)
✅ Answer: Apple = \$1.50, Pear = \$2.00
Set up the two equations:
\[15a + 10p = 42.5 \quad \cdots (1)\]
\[4a + 5p = 16 \quad \cdots (2)\]
Multiply equation (2) by 2 to match the \(10p\) coefficient:
\[8a + 10p = 32 \quad \cdots (3)\]
Subtract (3) from (1) to eliminate \(p\):
\[7a = 10.5 \implies a = 1.50\]
Substitute back into (2): \(4(1.5) + 5p = 16 \implies 6 + 5p = 16 \implies 5p = 10 \implies p = 2.00\)
✅ Answer: Apple = \$1.50, Pear = \$2.00
▶️ Answer/Explanation
Set up two equations from the given information:
\(4a + 20b = 130 \quad \cdots (1)\)
\(6a + 15b = 105 \quad \cdots (2)\)
Divide (1) by 2: \(2a + 10b = 65\). Divide (2) by 3: \(2a + 5b = 35\). Subtract to eliminate \(a\): \(5b = 30\), so \(b = 6\).
Substitute back: \(2a + 10(6) = 65 \Rightarrow 2a = 5 \Rightarrow a = 2.5\).
✅ Answer: \(a = 2.5,\quad b = 6\)
▶️ Answer/Explanation
Let the number Anna thought of be \(x\).
Multiplying it by \(2\) gives: \(2x\).
Finding the square root gives: \(\sqrt{2x}\).
We are told the result is \(12\), so we set up the equation:
\(\sqrt{2x} = 12\)
Square both sides to remove the square root:
\(2x = 144\)
Divide by \(2\):
\(x = 72\)
✅ Answer: \(72\)