James and Elizabeth buy some clothes - OCR - GCSE Maths - Question 21 - 2019 - Paper 1

To simplify the equations, we can solve the second equation for $j$:

$2j = 89 - 3s$

Dividing by 2 gives us:

$j = \frac{89 - 3s}{2}$

Now, substitute $j$ into the first equation:

$5s + 4\left(\frac{89 - 3s}{2}\right) = 163$

Multiplying through by 2 to eliminate the fraction gives us:

$10s + 4(89 - 3s) = 326$

This simplifies to:

$10s + 356 - 12s = 326$

Combining like terms results in:

$-2s + 356 = 326$

Now, solving for $s$:

$-2s = 326 - 356$

Thus, we find:

$-2s = -30$

This leads to:

$s = 15$

Now that we have the cost of one shirt, we can find the cost of one jumper using:

$j = \frac{89 - 3(15)}{2}$

This simplifies to:

$j = \frac{89 - 45}{2}$

Thus:

$j = \frac{44}{2} = 22$

Therefore, the cost of one shirt and one jumper are:

• Cost of one shirt £: 15
• Cost of one jumper £: 22