Joanna went school supply shopping. she spent $30.70 on notebooks and pencils. notebooks cost $2.20 each and pencils cost $1.09 each. she bought a total of 19 notebooks and pencils. how many of each did she buy?

Ok, so we need to set up a system of equations.

x + y = 19, where x is notebooks and y is pencils

2.2x + 1.09y = 30.70. You use the coefficient for individual prices and the total for the total given.

2.2x + 2.2y = 41.8  (multiply for elimination later)

2.2x + 1.09y = 30.7

1.11y = 11.1

y = 11.1/1.11

y = 10

Now we use the substitution method in x + y = 19

x + 10 = 19

x = 9

9 notebooks and 10 pencils

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1