you are in charge of bringing snacks to a picnic. you decide to buy grapes and pretzels. the grapes are $2.39 per pound and the pretzels cost $1.89 a bag. you have $11 to spend. write an equation that models to different amounts of grapes and pretzels that you can buy.
I think I need to write this in y=mx+b formula.. if that's possible..
y=-0.79x+4.60
is that right?
thanks in advance
You would first of all have to define what the x and y represent.
From your equation I concluded that
y is the number of pounds of grapes and x the number of pounds of pretzels.
Why is it necessary to change the equation to the form you have, I would write it as
189x + 239y = 1100
Your equation is correct.
Well, the equation you provided is not accurate for this scenario. To write an equation that represents the different amounts of grapes (x) and pretzels (y) you can buy, we need to consider the prices per pound and per bag, as well as the total budget.
Let's call the pounds of grapes "g" and the number of bags of pretzels "p". The equation can be written as:
2.39g + 1.89p = 11
So, for any combination of grapes and pretzels that you choose, the sum of the cost of grapes and pretzels should equal $11. Keep in mind that this equation doesn't represent a linear relationship, so it cannot be represented in the y=mx+b form.
To write an equation that models the different amounts of grapes (x) and pretzels (y) you can buy within the budget of $11, you need to consider the cost of each item.
1 pound of grapes costs $2.39, so the cost of grapes (in dollars) is 2.39x.
1 bag of pretzels costs $1.89, so the cost of pretzels (in dollars) is 1.89y.
Since you want to spend $11, the equation is:
2.39x + 1.89y = 11
This equation represents all the possible combinations of grapes and pretzels that you can buy within your budget. The equation you provided, y = -0.79x + 4.60, is not correct as it does not take into account the actual cost of the items or the budget.
To write an equation that models the different amounts of grapes and pretzels you can buy, you need to express the cost of the snacks in terms of the quantities you want to buy.
Let's say you buy 'g' pounds of grapes and 'p' bags of pretzels. The cost of the grapes would be $2.39 per pound, so the total cost of the grapes would be 2.39g dollars. Similarly, the cost of the pretzels would be $1.89 per bag, so the total cost of the pretzels would be 1.89p dollars.
To stay within your budget of $11, the equation can be written as:
2.39g + 1.89p ≤ 11
This equation represents the total cost of the grapes and pretzels being less than or equal to $11.
There is no need to use the y = mx + b formula in this case because we are not plotting a graph. Instead, we are modeling the cost constraints using an inequality.