![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXJ36oAlypDfaLMD7Oue2_8EeR1dKXOY0xfy3oUL6UoPPON4niCrr8VPjvTFbXl7ekBqAz6yinyefeCriL2ws3y3pMrY6yT0cl1qTmHplz92HWbR87jseWiYMI2nc3t3LpU-uXBwj33Gq1/s1600/image014.png)
Each box contains 3 apples and 4 pears. Applying a bit of maths terminology we could write this as (3 apples + 4 pears ) with the brackets showing that they are boxed together.
There are 5 boxes in the gift box or 5 × (3 apples + 4 pears )
There is a total of 5 × 3 apples and 5 × 4 pears or
5 × (3 apples + 4 pears ) = 5 × 3 apples + 5 × 4 pears = 15apples + 20pears.
Now instead of replacing the apples and pears with known numbers use xs and ys.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjH-M2tNvjANRy6r-p6eKKCzqJ3MSxj_-XWHlDtmkw9C23q0hOaUcELSvIeGwVb3_sqfO22xBpp4GBc5_6Sk63dQXnw_cpmsMs5QOX4yiAlzWvr7mDb6jdGVk3igyzEWugTG_vrdpDcF4aP/s1600/image008.png)
In maths this is 5×(3x + 4y) or 5(3x + 4y)
In total there 5×3x s and 5×4y s
or 5(3x + 4y)=5×3x + 5×4y=15x + 20y
In the Game of Maths we use holders rather than boxes.
In cards the following hands give the same result whatever numbers are declared for x and y.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYt4uuHEIy7E74vbypfbrutvMTOaZREJ71r3KzytkY7WqONUdPvWEfuLGV1aHXUfKBSFi_IkvYz7QTLH5ewbgaTi2-7EjLiD8O4dfJtZ2qA420MD2T5oLx8mN-KGJnJPVGHdrvPyA50ToQ/s1600/image020.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXm2T16nAUa0aVIIgQa4mjgkEwbQqUCN-jp7uJbbfUgBRH9MgpeJjsuhcDSZxpdRhHld4pGy02F8dnIdo9X0sPXUES0S7tWRosrdwt_gXbOlSA1-6GYadClVcSvvcAYhU_mJRgZi5qteqJ/s1600/image024.png)
Wherever there is a gap (or a change of card) above the long holder
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj378EwHaNzXZFomYsTjvTpAG0QS56q09BZs2MjkcnOU3pNVv6j9maruZxtHP7KUWw40ZqICyp1izhBJViGcg4Ahe35UZ3jMuPEYIv4VC9xQszSSDl-0fyzm9haQ6SfdCB-eyGapCvgGFTE/s1600/image028.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-nL9jy5OdyceKy0kgaQufWrcyH0BLIt1WWDACblmeaXfRSPR3QnlhF3FAIor_gT118yP_qKf0iwgE2rxZ96WFVOi1F28OnlKVD82f58-Uzn8C3-y-RbNdTJxD8Y0_r9dj1UZaal0uAtI2/s1600/image030.png)
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