Answer:
5 large boxes
3 small boxes
Step-by-step explanation:
Create two equations to represent the problem.
let "a" be the number of small boxes
let "b" be the number of large boxes
20a + 40b = 260 This equation shows the numbers of books
a + b = 8 This equations shows the number of boxes
Solve the system of equations (solve for a and b). We can solve using the substitution method.
Rearrange a + b = 8 to isolate one of the variables.
a = 8 - b New equation that represents "a"
Since we know an equation for "a", we can substitute what "a" equals into the other equation. There will only be one variable in the equation, so we can solve by isolating. Isolate by doing reverse operations.
Substitute "a" for 8 - b
20a + 40b = 260
20(8 - b) + 40b = 260 Distribute 20 over the brackets by multiplying
160 - 20b + 40b = 260 Collect like terms (numbers with same variables)
160 + 20b = 260 Start isolating "b". Subtract 160 from both sides
20b = 260 - 160
20b = 100 Divide both sides by 20
b = 5 Number of large boxes
Substitute "b" for 5 in the simplest equation
a + b = 8
a + 5 = 8 Subtract 5 from both sides to isolate "a"
a = 8 - 5
a = 3 Number of small boxes
Therefore there were 5 large boxes and 3 small boxes sent.
