word problem, i need help with this because my mom is working and cant help or else she'll get in trouble with work. also, this is 6th grade math.

Question

pablo and hector have pokemon cards in a ratio of 4:5. together they have 180 cards. how many cards does each boy have?

Answer 1

p/h = 4/5

p+h = 180

p = 180-h

(180-h)/h = 4/5

cross multiply

4h = 5(180-h) = 900-5h

4h+5h = 900

9h = 900

h =900/9 = 100 for Hector

p=180-h = 180-100 = 80 for Pablo

80/100 = 4/5

the ratio of Pablo's cards to Hector's cards is a constant, it remains the same, no matter how many cards each has

or you could rewrite the ratio in terms of the number of pablo's cards compared to the total of all cards

then

p/(p+h) = 4/(4+5) = 4/9

p/180= 4/9

cross multiply (multiply the numerator of the 1st fraction by the denominator of the 2nd fraction, and set it equal to the product of the numerator of the 2nd fraction multiplied by the denominator of the 1st fraction.)

9p = 4(180)

p =4(180/9) =4(20) = 80 for Pablo

h = 180-p = 180-80 = 100 for Hector

p/h =4/5 = 80/100