Find 4 consecutive even integers where the product of the two smaller numbers is 72 less than the product of the two larger numbers.

6, 8, 10, 12

Step-by-step explanation:

Given that x is the number, the 4 numbers would be

x, x + 2, x + 4, x + 6

so the two smallest numbers would be x and x + 2

and the two largest numbers would be x+4 and x+6

now set up an equation

x(x+2) = (x+4)(x+6) - 72

now FOIL

x^2 + 2x = x^2 + 6x + 4x + 24 - 72

combine like terms

x^2 + 2x = x^2 + 10x -48

subtract x^2 from both sides

2x = 10x - 48

subtract 2x from both sides

0 = 8x - 48

add 48 to both sides

48 = 8x

divide both sides by 8

6 = x

so the four numbers, x, x+2, x+4, and x+6 when you plug in x are equal to

6, 8, 10, 12

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!