Solving two-variable inequalities word problem

- 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 7/10 of a liter per plant. So this first term right over here, this is how much water used to water the sunflower plants and then the second term is how much water used to water the lily plants cause he needs half a liter for each of the L lily plants. And he has a total of 11 liters. So the sum right over here has to be less than or equal to 11. Alright. Ezra waters 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 gonna assume L is equal to 10. He waters 10 lily plants and each of them, he gives half a liter to. So 0.5, 0.5 x 10 is going to be 5. So it's gonna be 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 five from both sides. Subtract five 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 gonna just have 0.7 x S So this expression is the total amount of water he's gonna spend on the sunflower plants has to be less than or equal to 11- 5 is equal to six. And so now, we can divide both sides by 0.7 And we're gonna have to change the inequality because we are diving by a positive number, 0.7 So we're gonna get S... S is less than or equal to 6 ÷ 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 ÷ 7/10 which is equal to six times 10 over seven which is equal to 60/7 which is equal to what is this? 8 4/7 so S has to be less than eight and four sevenths. Now assuming that he's only, we're only thinking in terms of whole plants... (mumbles) integer numbers but actually whole numbers of plants and so, if S has to be less than 8 4/7, how many sunflower plants can he water at most with the remaining amount of water? Well, we'll say that he had, most he can water eight plants. We're gonna assume that he can't water just a fraction of a plant. He either waters something or he doesn't. So he's gonna water eight, he is gonna water eight plants. Cause that's the largest whole number that is less than 8 4/7. That satisfies... That is less than or equal to 8 4/7 I should say.