Question 3 of 18, step 1 of 1
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the difference between two positive integers is 2. if the smaller is added to the square of the larger, the sum is 88. find the integers.
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smaller integer = 7

The larger integer = 9

Step-by-step explanation:

* Lets explain how to solve the problem

- There are two integers

- Assume that the smaller is x and the larger is y

- The difference between them is 2

∵ The y is the larger and x is the smaller

∵ y - x = 2 ⇒ (1)

- If the smaller is added to the square of the larger, the sum is 88

∵ The square of the larger is y²

∴ x + y² = 88 ⇒ (2)

* Lets use the substitute method to solve the problem

- Use equation (1) to find x in terms of y

∵ y - x = 2 ⇒ add x to 2 sides and subtract 2 from both sides

∴ y - 2 = x ⇒ switch the two sides

∴ x = y - 2 ⇒ (3)

- Substitute x in equation (2) by equation (3)

∴ (y - 2) + y² = 88 ⇒ subtract 88 from both sides

∴ y - 2 + y² - 88 = 0 ⇒ add the like terms and arrange the terms

∴ y² + y - 90 = 0

* Lets factorize it

∵ y² = y × y

∵ 90 = 9 × 10

∵ y × 9 = 9y and y × 10 = 10y

∵ 10y - 9y = y

∴ y² + y - 90 = (y + 10)(y - 9)

∵ y² + y - 90 = 0

∴ (y + 10)(y - 9) = 0

- Equate each bracket by 0

∴ y + 10 = 0 and y - 9 = 0

∵ y + 10 = 0 ⇒ subtract 10 from both sides

∴ y = -10

∵ y - 9 = 0 ⇒ add 9 to both sides

∴ y = 9

∵ The numbers are positive we will rejected y = -10

∴ y = 9

- Substitute the values of y in equation (3) to find x

∵ x = y - 2

∴ x = 9 - 2 = 7

∴ x = 7

* The smaller integer = 7

* The larger integer = 9

linear

step-by-step explanation:

third choice down

step-by-step explanation:

the first inequality is based on the number of adults and campers, and the second inequality is based on the cost of feeding both the adult and the camper.

we know that there is room for 525 people max.   it's ok to have less than 525, but it's not ok to have more than 525, so the inequality is less than or equal to.   the number combination of adults (x) and campers (y) cannot exceed this 525 max.   therefore:

x + y ≤ 525

now we talk about cost.   it costs $9 to feed one adult, so depending upon the number of adults you have (x) depends upon how much it will cost to feed that number of adults.   same with the campers, who cost $5 to feed.   the adults can be represented by 9x and the campers can be represented by 5y.   since the budget cannot exceed 1,200, the second inequality is:

9x + 5y ≤ 1200