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# Solving two-variable inequalities word problem

CCSS.Math:

## Video transcript

Ezra enjoys gardening every sunflower plant he waters requires 0.7 liters of water and every lily plant he waters requires 0.5 liters of water Ezra has a total of 11 liters of water for these plants in the following inequality s represents the number of sunflower plants and L represents the number of lily plants Ezra can water see if this makes sense so it looks like so the number of sunflower plants is s and he would have to use seven tenths of a liter per plant so this first term right over here this is how much water used to to water the sunflower plants and then the second term is how much water used to water the lily plants because he needs half a liter for each of the L lily plants and he has a total of 11 liters so this sum right over here has to be less than or equal to 11 all right Ezra water is 10 lily plants so that's L is equal to 10 how many sunflower plants can he water at most with the remaining amount of water well let's think about this a little bit we have 0.7 0.7 times the number of sunflower plants he waters plus plus so we're going to swim L is equal to 10 he waters 10 lily plants and each of them he gives half a liter too so 0.5 0.5 times 10 is going to be 5 so it's going to be in five liters watering the 10 lily plants and this has to be less than or equal to 11 so we can try to isolate the s on the left-hand side so let's let's do that the number of sunflowers so we could first subtract 5 from both sides subtract 5 from both sides and we are going to be left with we are going to be left with on the left-hand side we're going to just have 0.7 times s so this expression this is a total amount of water he's going to spend on the sunflower plants has to be less than or equal to 11 minus 5 is equal to 6 and so now we can divide both sides 0.7 and we don't have to change the inequality because we are dividing by a positive number 0.7 so we're going to get s s is less than or equal to 6 divided by 0.7 or we could even write this as we could write this as well this is 6 divided by 0.7 let me write everything as a fraction this is the same thing as 6 divided by 7 tenths which is equal to 6 times 10 over 7 which is equal to 67 which is equal to what is this 8 and 4/7 so S has to be less than 8 and 4/7 now we're assuming that he's only we're only thinking in terms of whole playing a whole number integer numbers of plants are actually whole numbers of plants and so if s has to be less than 8 and 4/7 how many sudden flower plants can he water at most with the remaining amount of water well we'll say that he at most he can water 8 plants we're going to assume that he can't water just a fraction of a plant either water something or he doesn't so he's going to water 8 he is going to water 8 plants because that's the largest whole number that is less than 8 and 4/7 that satisfied that is less than or equal to 8 and 4/7 I should say