Answer:
The system of equations is x + y = 12 and 2x + 1.5y = 20
The number of packages of the hamburger is 4
The number of packages of the hotdog is 8
Step-by-step explanation:
Assume that they bringing x packages of hamburger y packages of hotdog
∵ x represents the number of packages of hamburger
∵ y represents the number of packages of hotdog
∵ Jimenez family is bringing 12 packages of hamburger and hotdog buns
∴ x + y = 12 ⇒ (1)
∵ The hamburger buns cost $2.00 per package
∵ The hot-dog buns cost $1.50 per package
∵ They spent $20 on the buns
∴ 2x + 1.5y = 20 ⇒ (2)
The system of equations is x + y = 12 and 2x + 1.5y = 20
Let us solve it to find x and y
→ Multiply equation (1) by -1.5 to make the coefficients of y equal in
values and different in signs to eliminate it
∵ -1.5(x) + -1.5(y) = -1.5(12)
∴ -1.5x - 1.5y = -18 ⇒ (3)
→ Add equations (2) and (3)
∵ (2x + -1.5) + (1.5y + -1.5y) = (20 + -18)
∴ 0.5x = 2
→ Divide both sides by 0.5 to find x
∴ x = 4
→ Substitute the value of x in equation (1) or (2) to find y
∵ 4 + y = 12
→ Subtract 4 from both sides
∴ 4 - 4 + y = 12 - 4
∴ y = 8
∴ The number of packages of the hamburger is 4
∴ The number of packages of the hotdog is 8
