The number of small packs is 2 and the number of large packs is 7
Step-by-step explanation:
A school is organizing a cookout where hot dogs will be served. The hot dogs come in small packs and large packs
- Each small pack has 8 hot dogs
- Each large pack has 18 hot dogs
- The school bought 5 more large packs than small packs, which altogether had 142 hot dogs
We need to find the number of small packs purchased and the number of large packs purchased
Assume that the number of the small packs is x and the number of the large pack is y
∵ There are x small packs
∵ Each small pack has 8 hot dogs
∵ There are y large packs
∵ Each large pack has 18 hot dogs
∴ The total number of hot dogs in all packs = 8x + 18y
∵ All packs had 142 hot dogs
- Equate the total number of hot doges by 142
∴ 8x + 18y = 142 ⇒ (1)
∵ The school bought 5 more large packs than small packs
∴ y = x + 5 ⇒ (2)
Now we have system of equations to solve it
Substitute y in equation (1) by equation (2)
∴ 8x + 18(x + 5) = 142
- Simplify the left hand side
∴ 8x + 18x + 90 = 142
- Add like terms in the left hand side
∴ 26x + 90 = 142
- Subtract 90 from both sides
∴ 26x = 52
- Divide both sides by 26
∴ x = 2
- Substitute the value of x in equation (2) to find y
∵ y = 2 + 5
∴ y = 7
The number of small packs is 2 and the number of large packs is 7
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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