Agym is in the process of purchasing new 5-pound and 8-pound dumbbells for their aerobics room. each 5-pound dumbbell costs $8 and each 8-pound dumbbell costs $12. the entire shipment of dumbbells costs $432 and weighs 282 pounds. which equations can be used to find the number of 5-pound dumbbells, x, and the number of 8-pound dumbbells, y, in the shipment?

$450 is the answer.

step-by-step explanation:

30% of 450 = 135

450-135=315

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°