Mr Wood makes tables with 4 legs, and stools with 3 legs.
Nine customers ordered 8 items each. Each order was different.
How many legs are needed altogether?
t tables and s stools
9 times 8 = 72 items
so
72 = t + s
now let's look at those 8 items
0 tables + 8 stools = 24 legs
1 table + 7 stools = 4+21 = 25 legs
2 tables + 6 stools = 8+18 = 26 legs
3 tables + 5 stolls = 12+15 = 27 legs
4 tables + 4 stools = 28
5 + 3 = 29
6 + 2 = 30
7 + 1 = 31
8 + 0 = 32
Well, look at that will you, 9 orders, all different of 8 items each. and the ONLY WAY you can do it.
so add
24 * 25 * 26 + ..... 32
I bet it is 9 times the middle one which is 4 tables, 4 stools for 28 legs
9 * 28 = 252 but be sure to check that :)
by the way
To calculate the total number of legs needed for the orders, we need to determine the number of tables and stools in each order and then multiply them by their respective number of legs.
Since each customer ordered 8 items and each order was different, we know that all 8 items in each order were either tables or stools. Also, we know that Mr Wood makes tables with 4 legs and stools with 3 legs.
To find out the number of tables and stools per order, we can set up a system of equations.
Let's assume 't' represents the number of tables and 's' represents the number of stools in an order.
From the given information, we have two equations:
Equation 1: t + s = 8 (because each order consisted of 8 items)
Equation 2: 4t + 3s = ? (we don't have the exact number of legs yet)
Now, we need to solve the system of equations to find the values of 't' and 's'. We can do this by substitution or elimination.
Let's use elimination:
Multiply Equation 1 by 3:
3(t + s) = 3(8)
3t + 3s = 24
Now, subtract Equation 2 from the new Equation 1:
(3t + 3s) - (4t + 3s) = 24 - ?
Simplifying:
3t + 3s - 4t - 3s = 24 - ?
Combining like terms:
-t = 24 - ?
Since we don't have the exact number of legs, we will leave the expression on the right-hand side as '?':
-t = 24 - ?
To find the value of '?', we need more information about the value of 't' or 's' in an order.
Please provide additional information so I can assist you further in determining the total number of legs needed.